Dirichlet problems with anisotropic principal part involving unbounded coefficients

Abstract

This article establishes the existence of solutions in a weak sense for a quasilinear Dirichlet problem exhibiting anisotropic differential operator with unbounded coefficients in the principal part and full dependence on the gradient in the lower order terms. A major part of this work focuses on the existence of a uniform bound for the solution set in the anisotropic setting. The unbounded coefficients are handled through an appropriate truncation and a priori estimates. For more information see https://ejde.math.txstate.edu/Volumes/2024/11/abstr.html