Harnack Inequalities for Nonuniformly Elliptic Divergence Structure Equations.
The main purpose of this work is to obtain a Harnack inequality and estimates for the Green function for the general class of degenerate elliptic operators described below.
We prove Harnack's inequality for non-negative solutions of some degenerate elliptic operators in divergence form with the lower order term coefficients satisfying a Kato type contition.
There is a long history of studying nonlinear boundary value problems for elliptic differential equations in a domain with sufficiently smooth boundary. In this paper, we show that the gradient of the solution of such a problem is continuous when a directional derivative is prescribed on the boundary of a Lipschitz domain for a large class of nonlinear equations under weak conditions on the data of the problem. The class of equations includes linear equations with fairly rough coefficients as well...
The aim of this paper is to show how, in order to prove regularity theorems, Hölder estimates, i.e. estimates involving products of powers of different semi-norms, can be used as well as standard estimates, and may in some instances be casier to prove.