A two-phase problem with degenerate operator in Orlicz-Sobolev spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915537191174144 |
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| author | Pontes, Pedro F. Silva Yang, Minbo |
| author_facet | Pontes, Pedro F. Silva Yang, Minbo |
| contents | In this paper we are interested in the study of a two-phase problem equipped with the $Φ$-Laplacian operator
$$ Δ_Φu \coloneqq \mbox{div} \left(ϕ(|\nabla u|)\dfrac{\nabla u}{|\nabla u|}\right),
$$
where
$Φ(s)=e^{s^2}-1$ and $ϕ=Φ'$. We obtain the existence, boundedness, and Log-Lipschitz regularity of the minimizers of the energy functional associated to the two-phase problem. Furthermore, we also prove that the phase change free boundaries of the minimizers possess a finite perimeter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17898 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A two-phase problem with degenerate operator in Orlicz-Sobolev spaces Pontes, Pedro F. Silva Yang, Minbo Analysis of PDEs In this paper we are interested in the study of a two-phase problem equipped with the $Φ$-Laplacian operator $$ Δ_Φu \coloneqq \mbox{div} \left(ϕ(|\nabla u|)\dfrac{\nabla u}{|\nabla u|}\right), $$ where $Φ(s)=e^{s^2}-1$ and $ϕ=Φ'$. We obtain the existence, boundedness, and Log-Lipschitz regularity of the minimizers of the energy functional associated to the two-phase problem. Furthermore, we also prove that the phase change free boundaries of the minimizers possess a finite perimeter. |
| title | A two-phase problem with degenerate operator in Orlicz-Sobolev spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.17898 |