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

2025/04/15 by Correa, Julio C., Prazeres, Disson dos
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/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 BV-inequality and the known classifications of blow-up profiles of the linear case.

Related

• Geometric properties of free boundaries in degenerate quenching problems
• A transmission problem for (p,q)-Laplacian
• Regularity in the two-phase Bernoulli problem for the p-Laplace operator
• Bounded minimizers of double phase problems at nearly linear growth
• A two-phase problem with degenerate operator in Orlicz-Sobolev spaces