Regularity and analyticity of solutions in a direction for elliptic equations

Yongyang Jin, Dongsheng Li and Xu-Jia Wang

Vol. 276 (2015), No. 2, 419–436

DOI: 10.2140/pjm.2015.276.419

Abstract

In this paper, we study the regularity and analyticity of solutions to linear elliptic equations with measurable or continuous coefficients. We prove that if the coefficients and inhomogeneous term are Hölder-continuous in a direction, then the second-order derivative in this direction of the solution is Hölder-continuous, with a different Hölder exponent. We also prove that if the coefficients and the inhomogeneous term are analytic in a direction, then the solution is analytic in that direction.

Keywords

Elliptic equation, analyticity, estimates, perturbation method

Mathematical Subject Classification 2010

Primary: 35J15

Secondary: 35B45

Milestones

Received: 14 July 2014

Revised: 27 October 2014

Accepted: 23 December 2014

Published: 15 July 2015