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 principal: Amster, Pablo Gustavo
Otros Autores: Mariani, María Cristina
Formato: Tesis doctoral publishedVersion
Lenguaje:Español
Publicado: Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales 1998
Materias:
CURVATURA MEDIA
ESPACIOS DE SOBOLEV
TEOREMAS DE PUNTO FIJO
OPERADOR ELIPTICO
MEAN CURVATURE
SOBOLEV SPACE
FIXED POINT THEOREMS
ELIPTIC OPERATOR
Acceso en línea:https://hdl.handle.net/20.500.12110/tesis_n3088_Amster
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id tesis:tesis_n3088_Amster
record_format dspace
spelling tesis:tesis_n3088_Amster2025-03-31T21:14:06Z Existencia y unicidad de soluciones para ecuaciones del tipo curvatura media prescripta Existence and uniqueness of the solutions of equations of prescribed mean curvature type Amster, Pablo Gustavo Mariani, María Cristina CURVATURA MEDIA ESPACIOS DE SOBOLEV TEOREMAS DE PUNTO FIJO OPERADOR ELIPTICO MEAN CURVATURE SOBOLEV SPACE FIXED POINT THEOREMS ELIPTIC OPERATOR 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. Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales 1998 info:eu-repo/semantics/doctoralThesis info:ar-repo/semantics/tesis doctoral info:eu-repo/semantics/publishedVersion application/pdf spa info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar https://hdl.handle.net/20.500.12110/tesis_n3088_Amster
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Español
orig_language_str_mv spa
topic CURVATURA MEDIA
ESPACIOS DE SOBOLEV
TEOREMAS DE PUNTO FIJO
OPERADOR ELIPTICO
MEAN CURVATURE
SOBOLEV SPACE
FIXED POINT THEOREMS
ELIPTIC OPERATOR
spellingShingle CURVATURA MEDIA
ESPACIOS DE SOBOLEV
TEOREMAS DE PUNTO FIJO
OPERADOR ELIPTICO
MEAN CURVATURE
SOBOLEV SPACE
FIXED POINT THEOREMS
ELIPTIC OPERATOR
Amster, Pablo Gustavo
Existencia y unicidad de soluciones para ecuaciones del tipo curvatura media prescripta
topic_facet CURVATURA MEDIA
ESPACIOS DE SOBOLEV
TEOREMAS DE PUNTO FIJO
OPERADOR ELIPTICO
MEAN CURVATURE
SOBOLEV SPACE
FIXED POINT THEOREMS
ELIPTIC OPERATOR
description 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.
author2 Mariani, María Cristina
author_facet Mariani, María Cristina
Amster, Pablo Gustavo
format Tesis doctoral
Tesis doctoral
publishedVersion
author Amster, Pablo Gustavo
author_sort Amster, Pablo Gustavo
title Existencia y unicidad de soluciones para ecuaciones del tipo curvatura media prescripta
title_short Existencia y unicidad de soluciones para ecuaciones del tipo curvatura media prescripta
title_full Existencia y unicidad de soluciones para ecuaciones del tipo curvatura media prescripta
title_fullStr Existencia y unicidad de soluciones para ecuaciones del tipo curvatura media prescripta
title_full_unstemmed Existencia y unicidad de soluciones para ecuaciones del tipo curvatura media prescripta
title_sort existencia y unicidad de soluciones para ecuaciones del tipo curvatura media prescripta
publisher Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales
publishDate 1998
url https://hdl.handle.net/20.500.12110/tesis_n3088_Amster
work_keys_str_mv AT amsterpablogustavo existenciayunicidaddesolucionesparaecuacionesdeltipocurvaturamediaprescripta
AT amsterpablogustavo existenceanduniquenessofthesolutionsofequationsofprescribedmeancurvaturetype
_version_ 1831982280823799808

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