A two-phase quenching-type problem for the p-Laplacian

Julio C. Correa; Disson dos Prazeres

paper

A two-phase quenching-type problem for the p-Laplacian

arXiv:2504.11370

Abstract

We study minimizers of non-differentiable functionals of the Alp-Phillips type with two-phases for the $p$ -Laplacian , focusing on the geometric and analytical properties of free boundaries. The main result establishes finite $(n - 1)$ -dimensional Hausdorff measure estimates, achieved through optimal gradient decay estimates, a $B V$ -inequality and the known classifications of blow-up profiles of the linear case.