Harnack inequality for a class of second-order degenerate elliptic equations

被引：0
作者：
Yu. A. Alkhutov
E. A. Khrenova
机构：
[1] Vladimir State University,
来源：
Proceedings of the Steklov Institute of Mathematics | 2012年 / 278卷
关键词：
Elliptic Equation; STEKLOV Institute; Sobolev Inequality; Harnack Inequality; Nonnegative Solution;
D O I：
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摘要：
A second-order degenerate elliptic equation in divergence form with a partially Muckenhoupt weight is studied. In a model case, the domain is divided by a hyperplane into two parts, and in each part the weight is a power function of |x| with the exponent less than the dimension of the space in absolute value. It is well known that solutions of such equations are Hölder continuous, whereas the classical Harnack inequality is missing. In this paper, we formulate and prove the Harnack inequality corresponding to the second-order degenerate elliptic equation under consideration.
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页码：1 / 9
页数：8
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