Existence Theory for a class of semilinear mixed local and nonlocal equations involving variable singularities and singular measures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916829102866432 |
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| author | Biswas, Sanjit Garain, Prashanta |
| author_facet | Biswas, Sanjit Garain, Prashanta |
| contents | This article establishes the existence of weak solutions for a class of mixed local-nonlocal problems with pure and perturbed singular nonlinearities. A key novelty is the treatment of variable singular exponents alongside measure-valued data. Notably, both source terms may be measures, with the singular component modeled by both a singular and non-singular measure. Our main focus is on the singular measure data, which appears to be new, even for constant exponents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04260 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence Theory for a class of semilinear mixed local and nonlocal equations involving variable singularities and singular measures Biswas, Sanjit Garain, Prashanta Analysis of PDEs 35M10, 35M12, 35J75, 35R06, 35R11 This article establishes the existence of weak solutions for a class of mixed local-nonlocal problems with pure and perturbed singular nonlinearities. A key novelty is the treatment of variable singular exponents alongside measure-valued data. Notably, both source terms may be measures, with the singular component modeled by both a singular and non-singular measure. Our main focus is on the singular measure data, which appears to be new, even for constant exponents. |
| title | Existence Theory for a class of semilinear mixed local and nonlocal equations involving variable singularities and singular measures |
| topic | Analysis of PDEs 35M10, 35M12, 35J75, 35R06, 35R11 |
| url | https://arxiv.org/abs/2507.04260 |