Article
| Title: | Existence and uniqueness for a two-dimensional Ventcel problem modeling the equilibrium of a prestressed membrane (English) |
| Author: | Greco, Antonio |
| Author: | Viglialoro, Giuseppe |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 68 |
| Issue: | 2 |
| Year: | 2023 |
| Pages: | 123-142 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | This paper deals with a mixed boundary-value problem of Ventcel type in two variables. The peculiarity of the Ventcel problem lies in the fact that one of the boundary conditions involves second order differentiation along the boundary. Under suitable assumptions on the data, we first give the definition of a weak solution, and then we prove that the problem is uniquely solvable. We also consider a particular case arising in real-world applications and discuss the resulting model. (English) |
| Keyword: | Ventcel boundary condition |
| Keyword: | Laplace-Beltrami operator |
| Keyword: | composite Sobolev space |
| Keyword: | well-posedness |
| MSC: | 35A01 |
| MSC: | 35A02 |
| MSC: | 35J25 |
| MSC: | 35M12 |
| idZBL: | Zbl 07675562 |
| idMR: | MR4574649 |
| DOI: | 10.21136/AM.2022.0095-21 |
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| Date available: | 2023-03-31T09:32:35Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151607 |
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