Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 11, pp. 1-13.

Title: Dirichlet problems with anisotropic principal part involving unbounded coefficients
       
Authors: Dumitru Motreanu (Univ. de Perpignan, France)
         Elisabetta Tornatore (Univ. of Palermo, Italy)

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.

Submitted March 16, 2023. Published January 30, 2024.
Math Subject Classifications: 35J70, 35J92.
Key Words: Anisotropic elliptic equation; anisotropic Sobolev space;
    unbounded  coefficient; bounded solution; truncation; pseudomonotone operator.