A free boundary problem for the p-Laplacian with nonlinear boundary conditions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913306159087616 |
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| author | Acampora, Paolo Cristoforoni, Emanuele |
| author_facet | Acampora, Paolo Cristoforoni, Emanuele |
| contents | We study a nonlinear generalization of a free boundary problem that arises in the context of thermal insulation. We consider two open sets $Ω\subseteq A$, and we search for an optimal $A$ in order to minimize a non-linear energy functional, whose minimizers $u$ satisfy the following conditions: $Δ_p u=0$ inside $A\setminusΩ$, $u=1$ in $Ω$, and a nonlinear Robin-like boundary $(p,q)$-condition on the free boundary $\partial A$. We study the variational formulation of the problem in SBV, and we prove that, under suitable conditions on the exponents $p$ and $q$, a minimizer exists and its jump set satisfies uniform density estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_10331 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A free boundary problem for the p-Laplacian with nonlinear boundary conditions Acampora, Paolo Cristoforoni, Emanuele Analysis of PDEs 35A01, 35J66, 35J92, 35R35 We study a nonlinear generalization of a free boundary problem that arises in the context of thermal insulation. We consider two open sets $Ω\subseteq A$, and we search for an optimal $A$ in order to minimize a non-linear energy functional, whose minimizers $u$ satisfy the following conditions: $Δ_p u=0$ inside $A\setminusΩ$, $u=1$ in $Ω$, and a nonlinear Robin-like boundary $(p,q)$-condition on the free boundary $\partial A$. We study the variational formulation of the problem in SBV, and we prove that, under suitable conditions on the exponents $p$ and $q$, a minimizer exists and its jump set satisfies uniform density estimates. |
| title | A free boundary problem for the p-Laplacian with nonlinear boundary conditions |
| topic | Analysis of PDEs 35A01, 35J66, 35J92, 35R35 |
| url | https://arxiv.org/abs/2206.10331 |