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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Detalles Bibliográficos
Autor: Amster, Pablo Gustavo
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
Descripción
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.