The dirichlet problem for the minimal surface equation on unbounded helicoidal domains of Rm
We consider a helicoidal group G in R n+1 and unbounded Ginvariant C 2,α-domains Ω ⊂ R n+1 whose helicoidal projections are exterior domains in R n, n ≥ 2. We show that for all s ∈ R, there exists a G-invariant solution us ∈ C 2,α Ω of the Dirichlet problem for the minimal surface equation with zero...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | Brasil |
| Institución: | Universidade Federal do Rio Grande do Sul (UFRGS) |
| Repositorio: | Biblioteca Digital de Teses e Dissertações da UFRGS |
| Idioma: | inglés |
| OAI Identifier: | oai:www.lume.ufrgs.br:10183/261995 |
| Acceso en línea: | http://hdl.handle.net/10183/261995 |
| Access Level: | acceso abierto |
| Palabra clave: | Problema de Dirichlet Helicóide Equação de superfície mínima Invariância de domínio Dirichlet problem Invariant domain Unbounded domains Invariant solutions Helicoidal group |
| Sumario: | We consider a helicoidal group G in R n+1 and unbounded Ginvariant C 2,α-domains Ω ⊂ R n+1 whose helicoidal projections are exterior domains in R n, n ≥ 2. We show that for all s ∈ R, there exists a G-invariant solution us ∈ C 2,α Ω of the Dirichlet problem for the minimal surface equation with zero boundary data which satisfies sup∂Ω |grad us| = |s|. Additionally, we provide further information on the behavior of these solutions at infinity. |
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