ShowMe Analysis Meeting 2004 June 3-5, 2004 University of Missouri Columbia, Missouri

Leonid Kovalev (Washington University)
Non-divergence elliptic equations with discontinuous coefficients

Abstract: We consider the Holder regularity of strong solutions of uniformly elliptic PDEs in two dimensions. According to a theorem of Morrey, such solutions possess first-order derivatives that are Holder continuous with exponent 1/K, where K is the ellipticity constant. We show that Morrey's exponent can be improved and offer a conjecture for the best possible exponent.