Boundary Blowup Solutions for the Finsler p-Laplacian: Wellposedness and Asymptotic Behaviour

TL;DR

This paper investigates boundary blow-up solutions for the Finsler p-Laplacian, establishing existence, uniqueness, and asymptotic behavior under a Keller-Osserman-type condition in smooth bounded domains.

Contribution

It introduces a Keller-Osserman-type condition for the Finsler p-Laplacian, extending classical results to anisotropic operators and analyzing boundary asymptotics.

Findings

Existence of boundary blow-up solutions under the Keller-Osserman condition.

Asymptotic estimates for solutions near the boundary.

Uniqueness results for power-type nonlinearities.

Abstract

We study the existence of large or boundary blow-up solutions to semilinear equations involving the Finsler p-Laplacian on bounded domains with sufficiently smooth boundaries. We establish a Keller-Osserman-type condition that ensures the existence of such solutions, and show that this condition retains the same integrability as that of the p-Laplacian. We examine the influence of the anisotropic norm underlying the Finsler p-Laplacian on the boundary behaviour of the solution, then derive asymptotic estimates for large solutions near the boundary of the domain. Using these boundary asymptotics, we prove uniqueness results for power type nonlinearities.