Robin problem with measure data and singular nonlinearities on the boundary
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911049389703168 |
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| author | Rozkosz, Andrzej |
| author_facet | Rozkosz, Andrzej |
| contents | We consider the Robin problem for a uniformly elliptic divergence operator with measure data on the right-hand side of the equation and an absorption term on the boundary involving blowing up terms. We prove the existence of a positive renormalized solution and provide it stochastic representation, which can be viwed as a generalized nonlinear Feynman-Kac formula. From this representation we derive some additional regularity results for the solution and some uniqueness results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robin problem with measure data and singular nonlinearities on the boundary Rozkosz, Andrzej Analysis of PDEs Primary 35J25, Secondary 35J65, 60H30 We consider the Robin problem for a uniformly elliptic divergence operator with measure data on the right-hand side of the equation and an absorption term on the boundary involving blowing up terms. We prove the existence of a positive renormalized solution and provide it stochastic representation, which can be viwed as a generalized nonlinear Feynman-Kac formula. From this representation we derive some additional regularity results for the solution and some uniqueness results. |
| title | Robin problem with measure data and singular nonlinearities on the boundary |
| topic | Analysis of PDEs Primary 35J25, Secondary 35J65, 60H30 |
| url | https://arxiv.org/abs/2507.07821 |