Existence and regularity of solutions of nonlinear anisotropic elliptic problem with Hardy potential

Article type: Research Article

Authors: Khelifi, Hichem^{a; b; c; *}

Affiliations: [a] Department of Mathematics, University of Algiers 1, Algiers, Algeria | [b] Laboratory of Mathematical Analysis and Applications, University of Algiers 1, Algiers, Algeria | [c] Laboratory of Nonliner Partial Differtial Equations and HM, ENS-Kouba, Algiers, Algeria

Correspondence: [*] Corresponding author. E-mail: khelifi.hichemedp@gmail.com.

Abstract: In this paper, we are interested in the existence and regularity of solutions for some anisotropic elliptic equations with Hardy potential and Lm(Ω) data in appropriate anisotropic Sobolev spaces. The aim of this work is to get natural conditions to show the existence and regularity results for the solutions, that is related to an anisotropic Hardy inequality.

Keywords: Anisotropic elliptic problems, existence and regularity, Hardy potential, irregular data, Hardy inequality

DOI: 10.3233/ASY-231889

Journal: Asymptotic Analysis, vol. 137, no. 3-4, pp. 291-303, 2024