Generalized Harnack Inequality for Nonhomogeneous Elliptic Equations

被引：13

作者：

Julin, Vesa ^{[1
]}

机构：

[1] Univ Jyvaskyla, Jyvaskyla, Finland

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2015年 / 216卷 / 02期

基金：

芬兰科学院;

关键词：

REGULARITY;

D O I：

10.1007/s00205-014-0817-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with nonlinear elliptic equations in nondivergence form F(D(2)u, Du, x) = 0 where F has a drift term which is not Lipschitz continuous. Under this condition the equations are nonhomogeneous and nonnegative solutions do not satisfy the classical Harnack inequality. This paper presents a new generalization of the Harnack inequality for such equations. As a corollary we obtain the optimal Harnack type of inequality for p(x)-harmonic functions which quantifies the strong minimum principle.

引用

页码：673 / 702

页数：30

共 24 条

[1] Regularity results for a class of functionals with non-standard growth [J].