Elliptic Regularity Theory: A First Course: 19 - Brossura

Beck, Lisa

Brossura

ISBN 10: 3319274848 ISBN 13: 9783319274843

Casa editrice: Springer, 2016

Riassunto

These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed. Finally, a short overview is given on the current state of the art concerning the size of the singular set on which discontinuities may occur.

The notes are intended for graduate and postgraduate students with a solid background in functional analysis and some familiarity with partial differential equations; they will also be of interest to researchers working on related topics.

Su questo libro

Dalla quarta di copertina

These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed. Finally, a short overview is given on the current state of the art concerning the size of the singular set on which discontinuities may occur.

The notes are intended for graduate and postgraduate students with a solid background in functional analysis and some familiarity with partial differential equations; they will also be of interest to researchers working on related topics.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2016
• Lingua: Inglese
• ISBN 10: 3319274848
• ISBN 13: 9783319274843
• Rilegatura: Copertina flessibile
• Numero edizione: 1
• Numero di pagine: 216
• Contatto del produttore: non disponibile
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