The two-phase Alt-Phillips problem for quasilinear operators

Yousef Alamri; José Miguel Urbano

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arXiv · 2604.05245

The two-phase Alt-Phillips problem for quasilinear operators

Yousef Alamri·José Miguel Urbano

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Abstract

We establish interior regularity and optimal growth estimates for sign-changing minimizers of the $p-$singular or $p-$degenerate quasilinear Alt--Phillips functional throughout the full range of $1<p<\infty$ and of the nonlinearity power $0<\gamma<p$. In addition, we obtain local finite perimeter and density estimates, from which we deduce the local $(N-1)$-rectifiability of the reduced and two-phase free boundaries and the local finiteness of their $(N-1)$-dimensional Hausdorff measure for a restricted range of $\gamma$.

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Yousef Alamri, José Miguel Urbano. 2026-04-06. The two-phase Alt-Phillips problem for quasilinear operators. https://arxiv.org/abs/2604.05245

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