The two-phase Alt-Phillips problem for quasilinear operators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913030723338240 |
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| author | Alamri, Yousef Urbano, José Miguel |
| author_facet | Alamri, Yousef Urbano, José Miguel |
| contents | 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 $0<γ<p$. 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 $γ$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_05245 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The two-phase Alt-Phillips problem for quasilinear operators Alamri, Yousef Urbano, José Miguel Analysis of PDEs Primary 35R35. Secondary 35A21, 35J70 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 $0<γ<p$. 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 $γ$. |
| title | The two-phase Alt-Phillips problem for quasilinear operators |
| topic | Analysis of PDEs Primary 35R35. Secondary 35A21, 35J70 |
| url | https://arxiv.org/abs/2604.05245 |