Global solvability of the Laplace equation in weighted Sobolev spaces
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866909951197184000 |
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| author | Bilalov, Bilal T. Nasibova, Natavan P. Softova, Lubomira G. Tramontano, Salvatore |
| author_facet | Bilalov, Bilal T. Nasibova, Natavan P. Softova, Lubomira G. Tramontano, Salvatore |
| contents | We consider a non-local boundary value problem for the Laplace equation in unbounded studding the weak and strong solvability of that problem in the framework of the weighted Sobolev space $W^{1,p}_ν$, with a Muckenhoupt weight. We proved that if any weak solution belongs to the space $W_ν^{2,p}$, then it is also a strong solution and satisfies the corespding boundary conditions. It should be noted that such problems do not fit into the general theory of elliptic equations and require a special technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07776 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global solvability of the Laplace equation in weighted Sobolev spaces Bilalov, Bilal T. Nasibova, Natavan P. Softova, Lubomira G. Tramontano, Salvatore Analysis of PDEs Functional Analysis 35A01, 35J05, 35K05, 42C15 We consider a non-local boundary value problem for the Laplace equation in unbounded studding the weak and strong solvability of that problem in the framework of the weighted Sobolev space $W^{1,p}_ν$, with a Muckenhoupt weight. We proved that if any weak solution belongs to the space $W_ν^{2,p}$, then it is also a strong solution and satisfies the corespding boundary conditions. It should be noted that such problems do not fit into the general theory of elliptic equations and require a special technique. |
| title | Global solvability of the Laplace equation in weighted Sobolev spaces |
| topic | Analysis of PDEs Functional Analysis 35A01, 35J05, 35K05, 42C15 |
| url | https://arxiv.org/abs/2307.07776 |