Existence, Non-Existence and Degeneracy of Limit Solutions to p-Laplace Problems Involving Hardy Potentials as p 1^+. The Case of A Critical Drift

Key Points

• This paper aims to analyze the behavior of solutions to specific p-Laplace problems as p approaches 1 from the right.
• Examined the asymptotic behavior of solutions satisfying a boundary value problem in a bounded open subset with a Lipschitz boundary.
• Considered the influence of critical drift and nonnegative data within the framework of Hardy potentials.
• Identified conditions under which limit solutions exist, do not exist, or show degeneracy as p approaches 1.
• Demonstrated unique behaviors of solutions influenced by the critical drift and the nature of the nonnegative datum.