Elliptic regularity theory [electronic resource] : a first course / Lisa Beck.
2016
QA377
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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
3319274856 (electronic book)
9783319274843
3319274848
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.
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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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Table of Contents
Preliminaries
Introduction to the Setting
The Scalar Case
Foundations for the Vectorial Case
Partial Regularity Results for Quasilinear Systems.
Introduction to the Setting
The Scalar Case
Foundations for the Vectorial Case
Partial Regularity Results for Quasilinear Systems.