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Título : | Minimización del primer valor propio del p-Laplaciano de Dirichlet en ciertos tipos de dominios = Minimization of the first eigenvalue of the Dirichlet p-Laplacian in certain classes of domains. |
Otros títulos : | Minimización del primer valor propio del p-Laplaciano de Dirichlet en ciertos tipos de dominios. |
Autor : | Mahadevan, Rajesh; supervisor de grado Toledo Oñate, Francisco Javier |
Palabras clave : | Espacios de Sobolev;Medidas de Hausdorff;Teoría de la Medida;Problema de Dirichlet |
Fecha de publicación : | 2012 |
Editorial : | Universidad de Concepción. |
Resumen : | In this thesis, we will work around the eigenvalue problem 8< : pu = jujp2u in u = 0 on @ where p is the p- Laplacian operator, with 1 < p < 1, which is a generalization of the Laplacian operator (p = 2) and it is defined for a function u in the Sobolev space W1;p 0 ( ) as pu = div(jrujp2ru): More specifically, we will study thoroughly the first eigenvalue 1( ) of p- Laplacian with Dirichlet condition, which is defined as the minimum of Rayleigh quotient for nonzero functions belonging to W1;p 0 ( ). i.e., 1( ) = min '2W1;p 0 ( );'6=0 R jr'jp R j'jp : We note that , 1 depends on the domain . We will show the principal properties of 1( ) and of its eigenfunctions, and later obtain results on the problem of minimization of 1( ) in certain classes of domains with the same volume or perimeter, similar to a classical problem. In the first chapter, which corresponds to the preliminaries, we will introduce some basic notions and definitions. We introduce the notion of a distribution, which allows us to define the concept of weak derivative of a function defined in a domain , among other notions. Moreover, in the first chapter we will define the Sobolev space W1;p( ), which is the set of all functions which belong to Lp( ), such that all its weak derivatives. |
Descripción : | Tesis para optar al grado de Magíster en Matemática. |
URI : | http://repositorio.udec.cl/jspui/handle/11594/5873 |
metadata.dc.source.uri: | https://go.openathens.net/redirector/udec.cl?url=http://tesisencap.udec.cl/concepcion/toledo_o_j/index.html |
Aparece en las colecciones: | Ciencias Físicas y Matemáticas - Tesis Magister |
Ficheros en este ítem:
Fichero | Descripción | Tamaño | Formato | |
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Tesis_Minimization of the first eigenvalue.pdf | 277,63 kB | Adobe PDF | Visualizar/Abrir |
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