Elliptic regularity theory [electronic resource] : a first course / Lisa Beck.
Beck, Lisa. author.
2016
QA377
Available Online

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Title Elliptic regularity theory [electronic resource] : a first course / Lisa Beck.
Author Beck, Lisa. author.
ISBN 9783319274850 (electronic book)
3319274856 (electronic book)
9783319274843
3319274848
DOI https://doi.org/10.1007/978-3-319-27485-0
Published Cham : Springer, 2016.
Language English
Description 1 online resource (xii, 201 pages).
Item Number 10.1007/978-3-319-27485-0 doi
Call Number QA377
Dewey Decimal Classification 515/.3533
Summary 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed April 12, 2016).
Series Lecture notes of the Unione Matematica Italiana ; 19.
Available in Other Form Print version: 9783319274843
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Preliminaries
Introduction to the Setting
The Scalar Case
Foundations for the Vectorial Case
Partial Regularity Results for Quasilinear Systems.

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