EAN: 9783319274843

ELLIPTIC REGULARITY THEORY - LISA BECK KARTONIE...

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.

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