Global Gradient Estimates for Nonlinear Elliptic Equations

Abstract

Abstract. We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calderón-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

Uniform estimates with data from generalized Lebesgue spaces in periodic structures

“…see [3,30]. Similar to the weighted Lebesgue spaces, there is a fundamental property of the Hardy-Littlewood maximal function in the Orlicz spaces.…”

“…see [30]. In these spaces, there is a fundamental property of the Hardy-Littlewood maximal function like Lemma 2.7 and Lemma 4.2, that is, there is a constant c = c(n, w, ) such that…”