Regularity and existence for semilinear mixed local-nonlocal equations with variable singularities and measure data
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912246671605760 |
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| author | Biswas, Sanjit Garain, Prashanta |
| author_facet | Biswas, Sanjit Garain, Prashanta |
| contents | This article proves the existence and regularity of weak solutions for a class of mixed local-nonlocal problems with singular nonlinearities. We examine both the purely singular problem and perturbed singular problems. A central contribution of this work is the inclusion of a variable singular exponent in the context of measure-valued data. Another notable feature is that the source terms in both the purely singular and perturbed components can simultaneously take the form of measures. To the best of our knowledge, this phenomenon is new, even in the case of a constant singular exponent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00755 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity and existence for semilinear mixed local-nonlocal equations with variable singularities and measure data Biswas, Sanjit Garain, Prashanta Analysis of PDEs 35M10, 35M12, 35J75, 35R06, 35R11, 35B65 This article proves the existence and regularity of weak solutions for a class of mixed local-nonlocal problems with singular nonlinearities. We examine both the purely singular problem and perturbed singular problems. A central contribution of this work is the inclusion of a variable singular exponent in the context of measure-valued data. Another notable feature is that the source terms in both the purely singular and perturbed components can simultaneously take the form of measures. To the best of our knowledge, this phenomenon is new, even in the case of a constant singular exponent. |
| title | Regularity and existence for semilinear mixed local-nonlocal equations with variable singularities and measure data |
| topic | Analysis of PDEs 35M10, 35M12, 35J75, 35R06, 35R11, 35B65 |
| url | https://arxiv.org/abs/2412.00755 |