Bethuel fabrice (29 risultati)

Lingua: Inglese
Editore: Birkhauser Basel, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
Da: Zubal-Books, Since 1961, Cleveland, OH, U.S.A.Zubal-Books, Since 1961
Contatta il venditoreVenditore con 5 stelleCondizione: Usato - Ottimo
EUR 45,08
EUR 4,01 spedizioneSpedito in U.S.A.Quantità: 1 disponibile
Condizione: Fine. *Price HAS BEEN REDUCED by 10% until Monday, Nov. 9 (weekend SALE item)* First edition, first printing, 189 pp., HARDCOVER (same isbn), previous owner's small hand stamp to front free endpaper else fine. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.…

Calculus of Variations and Geometric Evolution Problems : Lectures Given at the 2nd Session of the Centro Internazionale Estivo (C.I.M.E.) Held in Cetraro, Italy, June 15-22, 1996
Bethuel, Fabrice (EDT); Huisken, G.; Mueller, S.; Steffen, K.; Polden, A.; Dold, A. (EDT); Takens, F. (EDT); Teissier, B. (EDT); Hildebrandt, Stefan (EDT); Struwe, Michael (EDT)
- Brossura
Da: GreatBookPrices, Columbia, MD, U.S.A.GreatBookPrices
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 57,51
EUR 2,35 spedizioneSpedito in U.S.A.Quantità: Più di 20 disponibili
Condizione: New.

Calculus of Variations and Geometric Evolution Problems : Lectures Given at the 2nd Session of the Centro Internazionale Estivo (C.I.M.E.) Held in Cetraro, Italy, June 15-22, 1996
Bethuel, Fabrice (EDT); Huisken, G.; Mueller, S.; Steffen, K.; Polden, A.; Dold, A. (EDT); Takens, F. (EDT); Teissier, B. (EDT); Hildebrandt, Stefan (EDT); Struwe, Michael (EDT)
- Brossura
Da: GreatBookPrices, Columbia, MD, U.S.A.GreatBookPrices
Contatta il venditoreVenditore con 5 stelleCondizione: Usato - Come nuovo
EUR 60,99
EUR 2,35 spedizioneSpedito in U.S.A.Quantità: Più di 20 disponibili
Condizione: As New. Unread book in perfect condition.

- Brossura
Da: Antiquariat Renner OHG, Albstadt, GermaniaAntiquariat Renner OHG
Contatta il venditoreVenditore con 5 stelleMembro dell’associazione: BOEV
Condizione: Usato - Ottimo
EUR 25,00
EUR 45,00 spedizioneSpedito da Germania a U.S.A.Quantità: 1 disponibile
Softcover. Condizione: Sehr gut. Lectures Given at the 2nd Session of the C.I.M.E. held in Cetraro, Italy, June 15-22, 1996. Ed. by S. Hildebrandt & M. Struwe. Berlin, Springer (1999). 294 p. Pbck. Lecture Notes in Mathematics, 1713.- Contributions: F. Bethuel Variational Methods for Ginzburg-Landau Equations.- G. Huisken & A. Polden Geometric Evolution Equations for Hypersurfaces.- S. Müller Variational Models for Microstructure and Phase Transitions.- K. Steffen Parametric Surfaces of Prescribed Curvature.…

Calculus of Variations and Geometric Evolution Problems : Lectures Given at the 2nd Session of the Centro Internazionale Estivo (C.I.M.E.) Held in Cetraro, Italy, June 15-22, 1996
Bethuel, Fabrice (EDT); Huisken, G.; Mueller, S.; Steffen, K.; Polden, A.; Dold, A. (EDT); Takens, F. (EDT); Teissier, B. (EDT); Hildebrandt, Stefan (EDT); Struwe, Michael (EDT)
- Brossura
Da: GreatBookPricesUK, Woodford Green, Regno UnitoGreatBookPricesUK
Contatta il venditoreVenditore con 5 stelleCondizione: Usato - Come nuovo
EUR 67,86
EUR 17,98 spedizioneSpedito da Regno Unito a U.S.A.Quantità: Più di 20 disponibili
Condizione: As New. Unread book in perfect condition.

Calculus of Variations and Geometric Evolution Problems : Lectures Given at the 2nd Session of the Centro Internazionale Estivo (C.I.M.E.) Held in Cetraro, Italy, June 15-22, 1996
Bethuel, Fabrice (EDT); Huisken, G.; Mueller, S.; Steffen, K.; Polden, A.; Dold, A. (EDT); Takens, F. (EDT); Teissier, B. (EDT); Hildebrandt, Stefan (EDT); Struwe, Michael (EDT)
- Brossura
Da: GreatBookPricesUK, Woodford Green, Regno UnitoGreatBookPricesUK
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 68,06
EUR 17,98 spedizioneSpedito da Regno Unito a U.S.A.Quantità: Più di 20 disponibili
Condizione: New.

- Brossura
Da: Books Puddle, Woodside, NY, U.S.A.Books Puddle
Contatta il venditoreVenditore con 4 stelleCondizione: Nuovo
EUR 125,75
EUR 3,55 spedizioneSpedito in U.S.A.Quantità: 4 disponibili
Condizione: New.

- Brossura
Da: AHA-BUCH GmbH, Einbeck, GermaniaAHA-BUCH GmbH
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 95,62
EUR 35,00 spedizioneSpedito da Germania a U.S.A.Quantità: 1 disponibile
Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This bookpresents three short courses on topics at the intersection of Calculus of Variations, PDEs and Material Science, based on lectures given at the CIME summer school Variational and PDE Methods in Nonlinear Science , held in Cetraro (Italy), July 10 14, 2023.Fabrice Bethuel discusses aympototics for Allen Cahn systems, providing an overview of classical methods and tools for the scalar case and further results for the two-dimensional vectorial case. An alternate monotonicity formula is described, and the still open parabolic vectorial case is considered. Angkana Rüland considers the modelling and analysis of microstructures in shape-memory alloys, including material on quasiconvexity, differential inclusions, rigidity of the two-well problem under BV-regularity assumptions, and recent results on the quantitative dichotomy between rigidity and flexibility. Duvan Henao focuses on existence theory in nonlinear elasticity, where a central role is played by the Jacobian determinant. The methods developed have implications for the analysis of magnetoelasticity and nematic elastomers. The volume is aimed at graduate students and researchers interested in the applications of PDEs and the calculus of variations to the theory of phase transitions, fluid dynamics, materials science, and elasticity theory.…

Lingua: Inglese
Editore: Birkhäuser, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
Da: GreatBookPrices, Columbia, MD, U.S.A.GreatBookPrices
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 134,51
EUR 2,35 spedizioneSpedito in U.S.A.Quantità: 15 disponibili
Condizione: New.

Lingua: Inglese
Editore: Birkhauser Boston Inc, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
Da: Kennys Bookshop and Art Galleries Ltd., Galway, GY, IrlandaKennys Bookshop and Art Galleries Ltd.
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 130,79
EUR 9,50 spedizioneSpedito da Irlanda a U.S.A.Quantità: 15 disponibili
Condizione: New. The mathematics in this book apply directly to classical problems in superconductors, superfluids and liquid crystals. It should be of interest to mathematicians, physicists and engineers working on modern materials research. Series: Progress in Nonlinear Differential Equations and Their Applications. Num Pages: 190 pages, biography. BIC Classification: PBKJ; PBW. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 233 x 158 x 11. Weight in Grams: 298. . 1994. Paperback. . . . .…

Lingua: Inglese
Editore: Birkhäuser Verlag, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Rilegato
Da: Studibuch, Stuttgart, GermaniaStudibuch
Contatta il venditoreVenditore con 5 stelleCondizione: Usato - Molto buono
EUR 60,13
EUR 80,70 spedizioneSpedito da Germania a U.S.A.Quantità: 1 disponibile
hardcover. Condizione: Gut. 162 Seiten; 9783764337230.3 Gewicht in Gramm: 500.

Lingua: Inglese
Editore: Birkhäuser Boston, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
Da: Buchpark, Trebbin, GermaniaBuchpark
Contatta il venditoreVenditore con 5 stelleCondizione: Usato - Ottimo
AffarePrezzo corrente: EUR 50,33
EUR 105,00 spedizioneSpedito da Germania a U.S.A.Quantità: 2 disponibili
Condizione: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | The original motivation of this study comes from the following questions that were mentioned to one ofus by H. Matano. Let 2 2 G= B = {x=(X1lX2) E 2 ; x~ + x~ = Ixl < 1}. 1 Consider the Ginzburg-Landau functional 2 2 (1) E~(u) = ~ LIVul + 4~2 L(lu1 _1)2 which is defined for maps u E H1(G;C) also identified with Hl(G;R2). Fix the boundary condition 9(X) =X on 8G and set H; = {u E H1(G;C); u = 9 on 8G}. It is easy to see that (2) is achieved by some u~ that is smooth and satisfies the Euler equation in G, -~u~ = :2 u~(1 _lu~12) (3) { on aGo u~ =9 Themaximum principleeasily implies (see e.g., F. Bethuel, H. Brezisand F. Helein (2]) that any solution u~ of (3) satisfies lu~1 ~ 1 in G. In particular, a subsequence (u~.) converges in the w* - LOO(G) topology to a limit u*.…

Lingua: Inglese
Editore: Birkhäuser, 2017
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
Da: Revaluation Books, Exeter, Regno UnitoRevaluation Books
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 123,31
EUR 41,94 spedizioneSpedito da Regno Unito a U.S.A.Quantità: 1 disponibile
Paperback. Condizione: Brand New. 192 pages. 9.25x6.10x0.46 inches. In Stock.

Lingua: Inglese
Editore: Birkhäuser Verlag, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Rilegato
Da: Buchpark, Trebbin, GermaniaBuchpark
Contatta il venditoreVenditore con 5 stelleCondizione: Usato - Ottimo
AffarePrezzo corrente: EUR 57,03
EUR 105,00 spedizioneSpedito da Germania a U.S.A.Quantità: 1 disponibile
Condizione: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | Keine Beschreibung verfügbar.
Altre immaginiLingua: Inglese
Editore: Birkhäuser, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
Da: preigu, Osnabrück, Germaniapreigu
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 95,50
EUR 70,00 spedizioneSpedito da Germania a U.S.A.Quantità: 5 disponibili
Taschenbuch. Condizione: Neu. Ginzburg-Landau Vortices | Fabrice Bethuel (u. a.) | Taschenbuch | Progress in Nonlinear Differential Equations and Their Applications | xxvii | Englisch | 1994 | Birkhäuser | EAN 9780817637231 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.…

Lingua: Inglese
Editore: Birkhauser Boston Inc, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
Da: Kennys Bookstore, Olney, MD, U.S.A.Kennys Bookstore
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 168,20
EUR 9,35 spedizioneSpedito in U.S.A.Quantità: 15 disponibili
Condizione: New. The mathematics in this book apply directly to classical problems in superconductors, superfluids and liquid crystals. It should be of interest to mathematicians, physicists and engineers working on modern materials research. Series: Progress in Nonlinear Differential Equations and Their Applications. Num Pages: 190 pages, biography. BIC Classification: PBKJ; PBW. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 233 x 158 x 11. Weight in Grams: 298. . 1994. Paperback. . . . . Books ship from the US and Ireland.…

Lingua: Inglese
Editore: Birkhäuser, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
Da: Mispah books, Redhill, SURRE, Regno UnitoMispah books
Contatta il venditoreVenditore con 4 stelleCondizione: Usato - Come nuovo
EUR 229,59
EUR 29,96 spedizioneSpedito da Regno Unito a U.S.A.Quantità: 1 disponibile
Paperback. Condizione: Like New. LIKE NEW. SHIPS FROM MULTIPLE LOCATIONS. book.

Lingua: Inglese
Editore: Birkhäuser, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
Da: GreatBookPrices, Columbia, MD, U.S.A.GreatBookPrices
Contatta il venditoreVenditore con 5 stelleCondizione: Usato - Come nuovo
EUR 263,97
EUR 2,35 spedizioneSpedito in U.S.A.Quantità: 15 disponibili
Condizione: As New. Unread book in perfect condition.

Lingua: Inglese
Editore: Birkhäuser Verlag, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Rilegato
Da: BUCHSERVICE / ANTIQUARIAT Lars Lutzer, Wahlstedt, GermaniaBUCHSERVICE / ANTIQUARIAT Lars Lutzer
Contatta il venditoreVenditore con 5 stelleCondizione: Usato - Molto buono
EUR 259,90
EUR 39,95 spedizioneSpedito da Germania a U.S.A.Quantità: 1 disponibile
Condizione: gut. 1994. Ginzburg-Landau Vortices (Progress in Nonlinear Differential Equations and Their Applications) In deutscher Sprache. pages.

- Brossura
- Print on Demand
Da: Brook Bookstore On Demand, Napoli, NA, ItaliaBrook Bookstore On Demand
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 66,23
EUR 5,50 spedizioneSpedito da Italia a U.S.A.Quantità: Più di 20 disponibili
Condizione: new. Questo è un articolo print on demand.

Lingua: Inglese
Editore: Birkhäuser, 2017
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
- Print on Demand
Da: Brook Bookstore On Demand, Napoli, NA, ItaliaBrook Bookstore On Demand
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 62,23
EUR 20,00 spedizioneSpedito da Italia a U.S.A.Quantità: Più di 20 disponibili
Condizione: new. Questo è un articolo print on demand.

Lingua: Inglese
Editore: Springer, Berlin, Springer Nature Switzerland, European Mathematical Society, Università Degli Studi Di Napoli Federico II, Istituto Nazionale Di Alta Matematica Francesco Severi, Gruppo Nazionale Per L'analisi Matematica, La Probabilità E Le Loro Applicazioni, Università Degli Studi Di Verona, Springer, 2025
- Brossura
- Print on Demand
Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermaniaBuchWeltWeit Ludwig Meier e.K.
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 80,24
EUR 23,00 spedizioneSpedito da Germania a U.S.A.Quantità: 2 disponibili
Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This bookpresents three short courses on topics at the intersection of Calculus of Variations, PDEs and Material Science, based on lectures given at the CIME summer school Variational and PDE Methods in Nonlinear Science , held in Cetraro (Italy), July 10 14, 2023.Fabrice Bethuel discusses aympototics for Allen Cahn systems, providing an overview of classical methods and tools for the scalar case and further results for the two-dimensional vectorial case. An alternate monotonicity formula is described, and the still open parabolic vectorial case is considered. Angkana Rüland considers the modelling and analysis of microstructures in shape-memory alloys, including material on quasiconvexity, differential inclusions, rigidity of the two-well problem under BV-regularity assumptions, and recent results on the quantitative dichotomy between rigidity and flexibility. Duvan Henao focuses on existence theory in nonlinear elasticity, where a central role is played by the Jacobian determinant. The methods developed have implications for the analysis of magnetoelasticity and nematic elastomers. The volume is aimed at graduate students and researchers interested in the applications of PDEs and the calculus of variations to the theory of phase transitions, fluid dynamics, materials science, and elasticity theory. 189 pp. Englisch.…

Lingua: Inglese
Editore: Springer International Publishing, 2017
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
- Print on Demand
Da: moluna, Greven, Germaniamoluna
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 66,44
EUR 48,99 spedizioneSpedito da Germania a U.S.A.Quantità: Più di 20 disponibili
Kartoniert / Broschiert. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Affordable, softcover reprint of a classic textbookAuthors are well-known specialists in nonlinear functional analysis and partial differential equationsWritten in a clear, readable style with many examplesThis book is concerned .…

Lingua: Inglese
Editore: Birkhäuser Boston Mrz 1994, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
- Print on Demand
Da: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermaniaBuchWeltWeit Ludwig Meier e.K.
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 106,99
EUR 23,00 spedizioneSpedito da Germania a U.S.A.Quantità: 2 disponibili
Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The original motivation of this study comes from the following questions that were mentioned to one ofus by H. Matano. Let 2 2 G= B = {x=(X1lX2) E 2 ; x~ + x~ = Ixl 1}. 1 Consider the Ginzburg-Landau functional 2 2 (1) E~(u) = ~ LIVul + 4~2 L(lu1 _1)2 which is defined for maps u E H1(G;C) also identified with Hl(G;R2). Fix the boundary condition 9(X) =X on 8G and set H; = {u E H1(G;C); u = 9 on 8G}. It is easy to see that (2) is achieved by some u~ that is smooth and satisfies the Euler equation in G, -~u~ = :2 u~(1 _lu~12) (3) { on aGo u~ =9 Themaximum principleeasily implies (see e.g., F. Bethuel, H. Brezisand F. Helein (2]) that any solution u~ of (3) satisfies lu~1 ~ 1 in G. In particular, a subsequence (u~.) converges in the w - LOO(G) topology to a limit u . 196 pp. Englisch.…

- Brossura
- Print on Demand
Da: Majestic Books, Hounslow, Regno UnitoMajestic Books
Contatta il venditoreVenditore con 4 stelleCondizione: Nuovo
EUR 129,42
EUR 7,79 spedizioneSpedito da Regno Unito a U.S.A.Quantità: 4 disponibili
Condizione: New. Print on Demand.

Lingua: Inglese
Editore: Springer, Springer International Publishing Jul 2025, 2025
- Brossura
- Print on Demand
Da: buchversandmimpf2000, Emtmannsberg, BAYE, Germaniabuchversandmimpf2000
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 80,24
EUR 60,00 spedizioneSpedito da Germania a U.S.A.Quantità: 1 disponibile
Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book presents three short courses on topics at the intersection of Calculus of Variations, PDEs and Material Science, based on lectures given at the CIME summer school 'Variational and PDE Methods in Nonlinear Science', held in Cetraro (Italy), July 1014, 2023.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 200 pp. Englisch.…

- Brossura
- Print on Demand
Da: Biblios, frankfurt am main, HESSE, GermaniaBiblios
Contatta il venditoreVenditore con 4 stelleCondizione: Nuovo
EUR 131,22
EUR 9,95 spedizioneSpedito da Germania a U.S.A.Quantità: 4 disponibili
Condizione: New. PRINT ON DEMAND.

Lingua: Inglese
Editore: Birkhäuser Boston, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
- Print on Demand
Da: moluna, Greven, Germaniamoluna
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 92,27
EUR 48,99 spedizioneSpedito da Germania a U.S.A.Quantità: Più di 20 disponibili
Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. I. Energy estimates for S1-valued maps.- 1. An auxiliary linear problem.- 2. Variants of Theorem I.1.- 3. S1-valued harmonic maps with prescribed isolated singularities. The canonical harmonic map.- 4. Shrinking holes. Renormalized energy.- II. A lower boun.…

Lingua: Inglese
Editore: Birkhäuser, Birkhäuser Mär 1994, 1994
Serie: Libro 2 di 53 - Progress in Nonlinear Differential Equations and Their Applications
- Brossura
- Print on Demand
Da: buchversandmimpf2000, Emtmannsberg, BAYE, Germaniabuchversandmimpf2000
Contatta il venditoreVenditore con 5 stelleCondizione: Nuovo
EUR 106,99
EUR 60,00 spedizioneSpedito da Germania a U.S.A.Quantità: 1 disponibile
Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -I. Energy estimates for S1-valued maps.- 1. An auxiliary linear problem.- 2. Variants of Theorem I.1.- 3. S1-valued harmonic maps with prescribed isolated singularities. The canonical harmonic map.- 4. Shrinking holes. Renormalized energy.- II. A lower bound for the energy of S1-valued maps on perforated domains.- III. Some basic estimates for u .- 1. Estimates when G=BR and g(x)=x/|x|.- 2. An upper bound for E (u ).- 3. An upper bound for $$ frac{1}{{{varepsilon^2}}}{smallint_G}{left( {{{left| {{u_{varepsilon }}}ight|}^2} - 1}ight)^2} $$.- 4. $$ left| {{u_e}}ight| geqslant frac{1}{2} $$ on 'good discs'.- IV. Towards locating the singularities: bad discs and good discs.- 1. A covering argument.- 2. Modifying the bad discs.- V. An upper bound for the energy of u away from the singularities.- 1. A lower bound for the energy of u near aj.- 2. Proof of Theorem V.l.- VI. u n converges: u is born.- 1. Proof of Theorem VI.1.- 2. Further properties of u : singularities have degree one and they are not on the boundary.- VII. u coincides with THE canonical harmonic map having singularities (aj).- VIII. The configuration (aj) minimizes the renormalized energy W.- 1. The general case.- 2. The vanishing gradient property and its various forms.- 3. Construction of critical points of the renormalized energy.- 4. The case G=B1 and $$ gleft( hetaight) = {e^{{iheta }}} $$.- 5. The case G=B1 and $$ gleft( hetaight) = {e^{{iheta }}} $$ with d .- IX. Some additional properties of u .- 1. The zeroes of u .- 2. The limit of $$ left{ {{E_{varepsilon }}left( {{u_{varepsilon }}}ight) - pi dleft| {log varepsilon }ight|}ight} $$ as $$ varepsilon o 0 $$.- 3. $$ {smallint_G}{left| {abla left| {{u_{varepsilon }}}ight|}ight|^2} $$ remains bounded as $$ varepsilon o 0 $$.- 4. The bad discs revisited.- X. Non minimizing solutions of the Ginzburg-Landau equation.- 1. Preliminary estimates; bad discs and good discs.- 2. Splitting $$ left| {abla {v_{varepsilon }}}ight| $$.- 3. Study of the associated linear problems.- 4. The basic estimates: $$ {smallint_G}{left| {abla {v_{varepsilon }}}ight|^2} leqslant Cleft| {log ;varepsilon }ight| $$ and $$ {smallint_G}{left| {abla {v_{varepsilon }}}ight|^p} leqslant {C_p} $$ for pSpringer Nature c/o IBS, Benzstrasse 21, 48619 Heek 196 pp. Englisch. …