Lecture Notes of the Unione Matematica Italiana

Elliptic Regularity Theory

A First Course

Authors: Beck, Lisa

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  • 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
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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.

Reviews

“The whole text is equipped with many useful and interesting remarks, which helps make the lecture notes very readable. The book seems to be a solid contribution to understanding the problems of the regularity theory.” (Eugen Viszus, Mathematical Reviews, March, 2017)


Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-319-27485-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
  • ISBN 978-3-319-27484-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Elliptic Regularity Theory
Book Subtitle
A First Course
Authors
Series Title
Lecture Notes of the Unione Matematica Italiana
Series Volume
19
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-27485-0
DOI
10.1007/978-3-319-27485-0
Softcover ISBN
978-3-319-27484-3
Series ISSN
1862-9113
Edition Number
1
Number of Pages
XII, 201
Topics