A nonvariational form of the Neumann problem for the Poisson equation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914782988206080 |
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| author | de Cristoforis, M. Lanza |
| author_facet | de Cristoforis, M. Lanza |
| contents | We present a nonvariational setting for the Neumann problem for the Poisson equation for solutions that are Hölder continuous and that may have infinite Dirichlet integral. We introduce a distributional normal derivative on the boundary for the solutions that extends that for harmonic functions that has been introduced in a previous paper and we solve the nonvariational Neumann problem for data in the interior with a negative Schauder exponent and for data on the boundary that belong to a certain space of distributions on the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01818 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A nonvariational form of the Neumann problem for the Poisson equation de Cristoforis, M. Lanza Analysis of PDEs 31B20, 31B10, 35J25, 47B92 We present a nonvariational setting for the Neumann problem for the Poisson equation for solutions that are Hölder continuous and that may have infinite Dirichlet integral. We introduce a distributional normal derivative on the boundary for the solutions that extends that for harmonic functions that has been introduced in a previous paper and we solve the nonvariational Neumann problem for data in the interior with a negative Schauder exponent and for data on the boundary that belong to a certain space of distributions on the boundary. |
| title | A nonvariational form of the Neumann problem for the Poisson equation |
| topic | Analysis of PDEs 31B20, 31B10, 35J25, 47B92 |
| url | https://arxiv.org/abs/2405.01818 |