Dynamics of Partial Differential Equations

Volume 5 (2008)

Number 1

Regularity for quasi-linear elliptic systems with discontinuous coefficients

Pages: 87 – 99

DOI: http://dx.doi.org/10.4310/DPDE.2008.v5.n1.a4

Authors

Z. Feng (Department of Mathematics, University of Texas-Pan American, Edinburg, Texas, U.S.A.)

S. Zheng (Department of Mathematics, Beijing Jiaotong University, Beijing, China)

Abstract

In this paper we study regularity and partial regularity for theweak solution of a class of general quasi-linear elliptic equations and systems,which are of the quasi-linear main coefficients satisfying the VMO conditionsin x uniformly with respect to u, and of the lower order items satisfying controllablegrowth.

Keywords

VMO function, controllable growth, reserve Hölder inequality, partial regularity, weak solution

2010 Mathematics Subject Classification

35B45, 35J60

Full Text (PDF format)