Uniform $L^{\infty}$-boundedness for solutions of anisotropic quasilinear systems

TL;DR

This paper establishes uniform local $L^{ abla}$-boundedness estimates for solutions to complex anisotropic quasilinear systems with divergence form operators and critically growing nonlinearities.

Contribution

It introduces a method to obtain uniform $L^{ abla}$-bounds for solutions of non-autonomous anisotropic quasilinear systems with critical growth nonlinearities.

Findings

Established uniform local $L^{ abla}$-bounds for solutions.

Extended analysis to systems with critical nonlinear growth.

Applicable to non-autonomous divergence form operators.

Abstract

In this paper we obtain uniformly locally $L^{\infty}$-estimate of solutions to non-autonomous quasilinear system involving operators in divergence form and a family of nonlinearities that are allowed to grow also critically.