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arXiv · 2606.00538

Classification of blow-ups for the Alt--Phillips problem in three dimensions

Xavier Fernández-Real
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Abstract

We prove a flatness theorem for classical stable homogeneous solutions of the $\gamma$-Alt--Phillips free boundary problem in three dimensions in the range $0<\gamma\le 2/3$, where $\gamma$ is the exponent in the energy density $|\nabla u|^2+u^\gamma$. In particular, this implies full regularity of the free boundary for minimizers of the corresponding Alt--Phillips energy in dimension $3$.

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Xavier Fernández-Real. 2026-05-30. Classification of blow-ups for the Alt--Phillips problem in three dimensions. https://arxiv.org/abs/2606.00538

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