Electron. J. Differential Equations, Vol. 2024 (2024), No. 11, pp. 1-13.

Dirichlet problems with anisotropic principal part involving unbounded coefficients

Dumitru Motreanu, Elisabetta Tornatore

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.
DOI: 10.58997/ejde.2023.11

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Dumitru Motreanu
Département de Mathématiques
Université de Perpignan
66860 Perpignan, France
email: motreanu@univ-perp.fr
Elisabetta Tornatore
Department of Mathematics and Computer Science
University of Palermo
90123 Palermo, Italy
email: elisa.tornatore@unipa.it

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