Generalized Harnack's inequality for nonhomogeneous elliptic equations
Analysis of PDEs
2019-06-27 v2
Abstract
This paper is concerned with nonlinear elliptic equations in nondivergence form where the operator has a first order drift term which is not Lipschitz continuous. Under this condition the equations are nonhomogeneous and nonnegative solutions do not satisfy the classical Harnack's inequality. This paper presents a new type of generalization of the classical Harnack's inequality for such equations. As a corollary we obtain the optimal Harnack type of estimate for p(x)-harmonic functions which quantifies the strong minimum principle.
Cite
@article{arxiv.1311.3619,
title = {Generalized Harnack's inequality for nonhomogeneous elliptic equations},
author = {Vesa Julin},
journal= {arXiv preprint arXiv:1311.3619},
year = {2019}
}