Overview
- Gives a systematic, self-contained account of the topic
- Presents recent results for the first time
- Intended for researchers and graduate students with background in real and functional analysis
Part of the book series: Lecture Notes of the Unione Matematica Italiana (UMILN, volume 19)
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Table of contents (5 chapters)
Keywords
About this book
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.
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Bibliographic Information
Book Title: Elliptic Regularity Theory
Book Subtitle: A First Course
Authors: Lisa Beck
Series Title: Lecture Notes of the Unione Matematica Italiana
DOI: https://doi.org/10.1007/978-3-319-27485-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-27484-3Published: 18 April 2016
eBook ISBN: 978-3-319-27485-0Published: 08 April 2016
Series ISSN: 1862-9113
Series E-ISSN: 1862-9121
Edition Number: 1
Number of Pages: XII, 201
Topics: Partial Differential Equations, Calculus of Variations and Optimal Control; Optimization