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Campo DC | Valor | Lengua/Idioma |
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dc.contributor.advisor | Mahadevan, Rajesh; supervisor de grado | es |
dc.contributor.author | Toledo Oñate, Francisco Javier | es |
dc.date.accessioned | 2021-05-18T22:06:36Z | - |
dc.date.available | 2021-05-18T22:06:36Z | - |
dc.date.issued | 2012 | - |
dc.identifier.uri | http://repositorio.udec.cl/jspui/handle/11594/5873 | - |
dc.description | Tesis para optar al grado de Magíster en Matemática. | es |
dc.description.abstract | 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. | es |
dc.language.iso | eng | es |
dc.publisher | Universidad de Concepción. | es |
dc.rights | Creative Commoms CC BY NC ND 4.0 internacional (Atribución-NoComercial-SinDerivadas 4.0 Internacional) | - |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es | - |
dc.source.uri | https://go.openathens.net/redirector/udec.cl?url=http://tesisencap.udec.cl/concepcion/toledo_o_j/index.html | - |
dc.subject | Espacios de Sobolev | es |
dc.subject | Medidas de Hausdorff | es |
dc.subject | Teoría de la Medida | es |
dc.subject | Problema de Dirichlet | es |
dc.title | 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. | es |
dc.title.alternative | Minimización del primer valor propio del p-Laplaciano de Dirichlet en ciertos tipos de dominios. | en |
dc.type | Tesis | es |
dc.description.facultad | Facultad de Ciencias Físicas y Matemáticas | es |
dc.description.departamento | Departamento de Matemática. | es |
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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