Existencia y unicidad de soluciones para ecuaciones del tipo curvatura media prescripta
In this work we study the Dirichlet problem associated to the prescribedmean curvature equation. We obtain existence and local and global uniquenessfor the general and the nonparametric case under different conditions on the meancurvature H and the boundary data g. We also prove that if H and g ares...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 1998 |
| País: | Argentina |
| Institución: | Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales |
| Repositorio: | Biblioteca Digital (UBA-FCEN) |
| Idioma: | español |
| OAI Identifier: | tesis:tesis_n3088_Amster |
| Acceso en línea: | https://hdl.handle.net/20.500.12110/tesis_n3088_Amster |
| Access Level: | acceso abierto |
| Palabra clave: | CURVATURA MEDIA ESPACIOS DE SOBOLEV TEOREMAS DE PUNTO FIJO OPERADOR ELIPTICO MEAN CURVATURE SOBOLEV SPACE FIXED POINT THEOREMS ELIPTIC OPERATOR |
| Sumario: | In this work we study the Dirichlet problem associated to the prescribedmean curvature equation. We obtain existence and local and global uniquenessfor the general and the nonparametric case under different conditions on the meancurvature H and the boundary data g. We also prove that if H and g aresmooth, solutions are classic. Moreover, we prove in both cases that if there is asolution for some Ho and go , then there exists also a solution for H and g closeto Ho and go. We also study some semilinear equations of the type X’ = F(t,X) withboundary data X(0) = g(X(a)) , for which we obtain existence and uniquenessresults under some conditions on the continuous functions F and g. For theperiodic case (g = I), we give some criteria for the existence of solutions, and anuniqueness result. |
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