Vol. 276, No. 2, 2015

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ISSN: 0030-8730
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
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
Authors
Yongyang Jin
Department of Applied Mathematics
Zhejiang University of Technology
Hangzhou, 310023
China
Dongsheng Li
School of Mathematics and Statistics
Xi’an Jiaotong University
Xi’an, 710049
China
Xu-Jia Wang
Centre for Mathematics and Its Applications
Australian National University
Canberra ACT 0200
Australia