Regularity Theory - Department of Mathematics
www2.math.upenn.edu › ~qze › notesRegularity Theory Brian Krummel February 19, 2016 1 Interior Regularity We want to prove the following: Theorem 1. Let k 0 be an integer and 2(0;1). Let be an open set in Rn. Suppose u2C2() satis es Lu= aijD iju+ biD iu+ cu= fin for some elliptic operator Lwith coe cients aij;bi;c2Ck; () and some f 2Ck; (). Then u2Ck+2; () with juj k+2; ; 00 C(juj 0; 0 + jfj k; ;
Elliptic Regularity Theory | SpringerLink
link.springer.com › book › 10Introduction. 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.