Elliptic Regularity Theory

A First Course

Lisa Beck

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English

Springer International Publishing AG
18 April 2016

Real analysis, real variables; Differential calculus & equations; Calculus of variations

Series: Lecture Notes of the Unione Matematica Italiana

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.

By: Lisa Beck
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2016
Volume: 19
Dimensions: Height: 235mm, Width: 155mm, Spine: 12mm
Weight: 3.343kg
ISBN: 9783319274843
ISBN 10: 3319274848
Series: Lecture Notes of the Unione Matematica Italiana
Pages: 201
Publication Date: 18 April 2016
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Preliminaries.- Introduction to the Setting.- The Scalar Case.- Foundations for the Vectorial Case.- Partial Regularity Results for Quasilinear Systems.

Reviews for Elliptic Regularity Theory: A First Course

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)