Global regularity of solutions to quasilinear conormal derivative problem with controlled growth

TL;DR

This paper establishes the global regularity of weak solutions to a class of quasilinear elliptic boundary value problems with conormal derivatives, under controlled growth and small oscillation conditions on coefficients.

Contribution

It proves the global regularity of solutions for quasilinear elliptic equations with BMO coefficients and controlled growth, extending regularity results to Lipschitz domains.

Findings

Solutions are globally regular under specified conditions.

Leading coefficients have small mean oscillations.

Results apply to Lipschitz domains.

Abstract

We prove the global regularity of weak solutions to the conormal derivative boundary value problem for quasilinear elliptic equations in divergence form on Lipschitz domains under the controlled growth conditions on the low order terms. The leading coefficients are in the class of BMO functions with small mean oscillations.