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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.20011 |
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| _version_ | 1866929440578076672 |
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| author | Campos, Pedro Miguel Rodrigues, José Francisco |
| author_facet | Campos, Pedro Miguel Rodrigues, José Francisco |
| contents | In this work we study an inhomogeneous two-phase obstacle-type problem associated to the $s$-fractional $p$-Laplacian. Besides the existence and uniqueness of solutions, we study the convergence of the solutions when $s\to 1$ to the classical problem. We also study the continuous dependence with respect to the level-set function $v$, yielding an existence result for a two-phase obstacle-type problem with an implicit level-set function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20011 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An implicit two-phase obstacle-type problem for the $p$-Laplacian with the fractional gradient Campos, Pedro Miguel Rodrigues, José Francisco Analysis of PDEs In this work we study an inhomogeneous two-phase obstacle-type problem associated to the $s$-fractional $p$-Laplacian. Besides the existence and uniqueness of solutions, we study the convergence of the solutions when $s\to 1$ to the classical problem. We also study the continuous dependence with respect to the level-set function $v$, yielding an existence result for a two-phase obstacle-type problem with an implicit level-set function. |
| title | An implicit two-phase obstacle-type problem for the $p$-Laplacian with the fractional gradient |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.20011 |