Elliptic Regularity Theory

A First Course

  • Lisa Beck

Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 19)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Lisa Beck
    Pages 1-52
  3. Lisa Beck
    Pages 53-58
  4. Lisa Beck
    Pages 59-84
  5. Lisa Beck
    Pages 85-128
  6. Back Matter
    Pages 181-203

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.


35J47,35B65,49N60 quasilinear elliptic systems weak solutions (partial) regularity dimension reduction optimality

Authors and affiliations

  • Lisa Beck
    • 1
  1. 1.Institut für MathematikUniversität AugsburgAugsburgGermany

Bibliographic information