Existencia y unicidad de soluciones para ecuaciones del tipo curvatura media prescripta

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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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Autor principal: Amster, Pablo
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
http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=aextesis&d=tesis_n3088_Amster_oai
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spelling I28-R145-tesis_n3088_Amster_oai2023-04-26 Mariani, María Cristina Amster, Pablo 1998 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. application/pdf https://hdl.handle.net/20.500.12110/tesis_n3088_Amster spa Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar CURVATURA MEDIA ESPACIOS DE SOBOLEV TEOREMAS DE PUNTO FIJO OPERADOR ELIPTICO MEAN CURVATURE SOBOLEV SPACE FIXED POINT THEOREMS ELIPTIC OPERATOR 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 info:eu-repo/semantics/doctoralThesis info:ar-repo/semantics/tesis doctoral info:eu-repo/semantics/publishedVersion http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=aextesis&d=tesis_n3088_Amster_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (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
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
format Tesis doctoral
Tesis doctoral
publishedVersion
author Amster, Pablo
author_sort Amster, Pablo
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
http://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=aextesis&d=tesis_n3088_Amster_oai
work_keys_str_mv AT amsterpablo existenciayunicidaddesolucionesparaecuacionesdeltipocurvaturamediaprescripta
AT amsterpablo existenceanduniquenessofthesolutionsofequationsofprescribedmeancurvaturetype
_version_ 1766015502652538880

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