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Paperback. Condizione: new. Paperback. In this thesis, we study the regularity of optimal transport maps and its applications to the semi-geostrophic system. The first two chapters survey the known theory, in particular there is a self-contained proof of Brenier theorem on existence of optimal transport maps and of Caffarellis Theorem on Holder continuity of optimal maps. In the third and fourth chapter we start investigating Sobolev regularity of optimal transport maps, while in Chapter 5 we show how the above mentioned results allows to prove the existence of Eulerian solution to the semi-geostrophic equation. In Chapter 6 we prove partial regularity of optimal maps with respect to a generic cost functions (it is well known that in this case global regularity can not be expected). More precisely we show that if the target and source measure have smooth densities the optimal map is always smooth outside a closed set of measure zero. In this thesis, we study the regularity of optimal transport maps and its applications to the semi-geostrophic system. The first two chapters survey the known theory, in particular there is a self-contained proof of Brenier theorem on existence of optimal transport maps and of Caffarellis Theorem on Holder continuity of optimal maps. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
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Aggiungi al carrelloPaperback. Condizione: New. 1st ed. 2021. This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school "Geometric Measure Theory and Applications - From Geometric Analysis to Free Boundary Problems" which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro.Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.
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Aggiungi al carrelloPaperback. Condizione: New. 1st ed. 2021. This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school "Geometric Measure Theory and Applications - From Geometric Analysis to Free Boundary Problems" which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro.Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.
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Aggiungi al carrelloCondizione: Sehr gut. Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | In this thesis, we study the regularity of optimal transport maps and its applications to the semi-geostrophic system. The first two chapters survey the known theory, in particular there is a self-contained proof of Brenier' theorem on existence of optimal transport maps and of Caffarelli's Theorem on Holder continuity of optimal maps. In the third and fourth chapter we start investigating Sobolev regularity of optimal transport maps, while in Chapter 5 we show how the above mentioned results allows to prove the existence of Eulerian solution to the semi-geostrophic equation. In Chapter 6 we prove partial regularity of optimal maps with respect to a generic cost functions (it is well known that in this case global regularity can not be expected). More precisely we show that if the target and source measure have smooth densities the optimal map is always smooth outside a closed set of measure zero.
Lingua: Inglese
Editore: Springer International Publishing, Springer Nature Switzerland, 2021
ISBN 10: 3030657981 ISBN 13: 9783030657987
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Aggiungi al carrelloTaschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school 'Geometric Measure Theory and Applications - From Geometric Analysis to Free Boundary Problems' which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro.Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.
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Aggiungi al carrelloTaschenbuch. Condizione: Neu. Geometric Measure Theory and Free Boundary Problems | Cetraro, Italy 2019 | Guido De Philippis (u. a.) | Taschenbuch | Lecture Notes in Mathematics | v | Englisch | 2021 | Springer | EAN 9783030657987 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
Lingua: Inglese
Editore: American Mathematical Society, 2024
ISBN 10: 1470466953 ISBN 13: 9781470466954
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Aggiungi al carrellopaperback. Condizione: Sehr gut. 166 Seiten; 9781470466954.2 Gewicht in Gramm: 500.
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