Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Imbert, Cyril

关键词: Degenerate fully non-linear elliptic equation;    Singular fully non-linear elliptic equation;    Non-divergence form;    Alexandroff-Bakelman-Pucci estimate;    Weak Harnack inequality;    Local maximum principle;    Harnack inequality;    Holder regularity;    Viscosity solutions;   

DOI  :  10.1016/j.jde.2010.07.005

来源: Elsevier

【 摘 要 】

In this paper, we study fully non-linear elliptic equations in non-divergence form which can be degenerate or singular when the gradient is small. Typical examples are either equations involving the m-Laplace operator or Bellman-lsaacs equations from stochastic control problems. We establish an Alexandroff-Bakelman-Pucci estimate and we prove a Harnack inequality for viscosity solutions of such non-linear elliptic equations. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free