Methods and Applications of Analysis

Volume 18 (2011)

Number 4

$C^{1,1}$ estimates for elliptic equations with partial and piecewise continuous coefficients

Pages: 373 – 390

DOI: https://dx.doi.org/10.4310/MAA.2011.v18.n4.a2

Author

Jingang Xiong (LMCS, School of Mathematical Sciences, Beijing Normal University, Beijing, China)

Abstract

In the paper, we establish existence, uniqueness and optimal $C^{1,1}$ regularity of $L^p$-viscosity solutions of Dirichlet problem of linear elliptic equations with partially and piecewise Hölder coefficients. For piecewise Hölder coefficients, our $C^1,1$ estimates are independent of the distance between interfaces of discontinuity of the coefficients.

Keywords

discontinuous coefficients, uniqueness, C1,1 estimates

2010 Mathematics Subject Classification

35J15

Published 23 July 2012