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arXiv · 2504.11370

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

Julio C. Correa·Disson dos Prazeres
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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.

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Julio C. Correa, Disson dos Prazeres. 2025-04-15. A two-phase quenching-type problem for the p-Laplacian. https://arxiv.org/abs/2504.11370

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