Riyadh Nesraoui, Hichem Khelifi

Regularity of Solutions to $\vec{p}$-Laplacian Problem with a Lower Order Term and a Hardy Potential

abstract:
In this paper, we study the existence and regularity results for an anisotropic elliptic problem involving a lower order term and a Hardy potential. Interestingly, our study reveals that the use of the Hardy inequality is dispensable due to the inclusion of the lower order term, which dominates the Hardy term. This inclusion not only improves the regularity of solutions but also eli\-mi\-na\-tes the need to impose constraints on the coefficient of the Hardy term.

Mathematics Subject Classification: 35J60, 35B45, 35D30, 35B65

Key words and phrases: Anisotropic problems, lower order terms, Hardy potential, $L^{m}$ data, fixed point theorem