Stability of complement value problems for $p$-Lévy operators
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910835078594560 |
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| author | Foghem, Guy |
| author_facet | Foghem, Guy |
| contents | We set up a general framework tailor-made to solve complement value problems governed by symmetric nonlinear integrodifferential $p$-Lévy operators. A prototypical example of integrodifferential $p$-Lévy operators is the well-known fractional $p$-Laplace operator. Our main focus is on nonlinear IDEs in the presence of Dirichlet, Neumann and Robin conditions and we show well-posedness results. Several results are new even for the fractional $p$-Laplace operator but we develop the approach for general translation-invariant nonlocal operators. We also bridge a gap from nonlocal to local, by showing that solutions to the local Dirichlet and Neumann boundary value problems associated with $p$-Laplacian are strong limits of the nonlocal ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03776 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability of complement value problems for $p$-Lévy operators Foghem, Guy Analysis of PDEs 35D30, 35B35, 35J60, 35J66 We set up a general framework tailor-made to solve complement value problems governed by symmetric nonlinear integrodifferential $p$-Lévy operators. A prototypical example of integrodifferential $p$-Lévy operators is the well-known fractional $p$-Laplace operator. Our main focus is on nonlinear IDEs in the presence of Dirichlet, Neumann and Robin conditions and we show well-posedness results. Several results are new even for the fractional $p$-Laplace operator but we develop the approach for general translation-invariant nonlocal operators. We also bridge a gap from nonlocal to local, by showing that solutions to the local Dirichlet and Neumann boundary value problems associated with $p$-Laplacian are strong limits of the nonlocal ones. |
| title | Stability of complement value problems for $p$-Lévy operators |
| topic | Analysis of PDEs 35D30, 35B35, 35J60, 35J66 |
| url | https://arxiv.org/abs/2303.03776 |