{"id":130998,"date":"1996-01-01T00:00:00","date_gmt":"1996-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/valores-propios-del-laplaciano-y-geometria-isoperimetrica\/"},"modified":"1996-01-01T00:00:00","modified_gmt":"1996-01-01T00:00:00","slug":"valores-propios-del-laplaciano-y-geometria-isoperimetrica","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/valores-propios-del-laplaciano-y-geometria-isoperimetrica\/","title":{"rendered":"Valores propios del laplaciano y geometria isoperimetrica."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Albert Avi\u00f1o Andres <\/strong><\/h2>\n<p>Este trabajo ha estado motivado por el estudio de los valores propios del laplaciano sobre un dominio del espacio euclideo. Esto nos ha llevado a estudiar ciertos problemas isoperimetricos que tambien tienen interes por ellos mismos.  en la primera parte de la memoria se hace un resumen de diversos resultados de la teoria geometrica de la medida y del analisis funcional necesarios para el desarrollo posterior del trabajo: conjuntos normalizados, diferentes nociones de frontera, funciones de variacion acotada y conjuntos con perimetro finito.  la segunda parte esta dedicada al estudio de una variante del problema isoperimetrico restringido. Mas concretamente nos hemos interesado por el tema de la existencia y propiedades de los conjuntos minimizadores, asi como por la obtencion de diversas estimaciones para el valor minimo de dicha variante.  la tercera parte contiene diversas acotaciones inferiores para los valores propios del laplaciano que amplian, generalizan y, en ciertos casos, mejoran los resultados obtenidos por cheeger (1970). En el ultimo capitulo estos resultados han sido extendidos a otros dos problemas de valores propios: el caso semilineal del operador de laplace y el caso del p-laplaciano.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Valores propios del laplaciano y geometria isoperimetrica.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Valores propios del laplaciano y geometria isoperimetrica. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Albert Avi\u00f1o Andres <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Aut\u00f3noma de barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1996<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Xavier Mora Gin\u00e9<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Carles Perello  I Valls <\/li>\n<li> Diaz Diaz Jes\u00fas Ildefonso (vocal)<\/li>\n<li>Joan Llu\u00eds Cerd\u00ed\u00a0 Mart\u00edn (vocal)<\/li>\n<li>Joan Sol\u00ed\u00a0-morales Rubio (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Albert Avi\u00f1o Andres Este trabajo ha estado motivado por el estudio de los valores propios del laplaciano [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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