On the behavior of solution of nonlinear equations

TL;DR

This paper investigates the behavior of solutions to nonlinear elliptic equations, establishing a Wiener criterion for the mixed boundary problem, which advances understanding of boundary regularity in nonlinear PDEs.

Contribution

It introduces a Wiener criterion specifically for the mixed boundary problem in nonlinear second-order elliptic equations, a novel extension in the field.

Findings

Established Wiener criterion for nonlinear elliptic boundary problems

Provided conditions for boundary regularity of solutions

Extended classical results to nonlinear context

Abstract

In this paper we establish of the Wiener criterion for solution the mixed boundary problem for nonlinear elliptic equation of second order.