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DOI: 10.46698/c8515-1572-8469-r
Existence and Uniqueness of Solution for Nonlinear Anisotropic Elliptic Dirichlet Problems
Naceri, M.
Vladikavkaz Mathematical Journal 2026. Vol. 28. Issue 1.
Abstract: We consider boundary value problem for nonlinear anisotropic elliptic partial differential equations in bounded open Lipschitz domain and the Dirichlet boundary conditions. We also suppose that the body force function belongs to the natural dual space under certain hypotheses regarding the nonlinear anisotropic operators present on the main side of the proposed problems. We prove the existence and uniqueness of a weak solution in anisotropic Sobolev space for this problem. Our proofs are based on various anisotropic Sobolev inequalities, embedding theorems, and features of pseudo-monotone operators. The functional setting involves anisotropic Lebesgue and Sobolev spaces in the scalar case and their most important properties.
For citation: Naceri, M. Existence and Uniqueness of Solution for Nonlinear Anisotropic Elliptic Dirichlet Problems, Vladikavkaz Math. J., 2026, vol. 28, no.1, pp.122-133. DOI 10.46698/c8515-1572-8469-r
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