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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2017.tde-06122017-104037
Document
Author
Full name
Ariadne Nogueira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2017
Supervisor
Committee
Pereira, Marcone Corrêa (President)
Aragão, Gleiciane da Silva
Carbinatto, Maria do Carmo
Carvalho, Alexandre Nolasco de
Pereira, Antonio Luiz
Title in Portuguese
Integrais concentradas na fronteira e aplicações para problemas elípticos semilineares
Keywords in Portuguese
Equações diferenciais parciais
Equações elípticas
Integrais concentradas
Perturbação de contorno
Semi-continuidade superior e inferior de soluções
Abstract in Portuguese
Neste trabalho estudamos propriedades de integrais concentradas, ou seja, integrais cujo integrando atua apenas em uma vizinhança do domínio em questão. Tais termos são utilizados para conhecer o comportamento do integrando em regiões cuja medida de Lebesgue se aproxima de zero quando um parâmetro tende a zero. Ilustraremos estes resultados abstratos através de duas aplicações, ambas em domínios Lipschitz de R2, onde adicionamos um termo de concentração em problemas semilineares elípticos: domínio com fronteira oscilante que tende a um domínio limite fixo; e domínio do tipo fino com fronteira oscilante. Em ambos os casos, provamos a semicontinuidade superior e inferior da família de soluções dos problemas.
Title in English
Concentrating integrals and applications for semilinear elliptic problems
Keywords in English
Boundary perturbations
Concentrating integrals
Partial differential equations
Semilinear elliptic equations
Upper and lower semicontinuity of solutions
Abstract in English
In this work we study concentrating integrals properties, in other words, we analyze integrals which function that is been integrated acts only in a neighborhood of the boundary of the domain. Such terms are use to know the behaviour of the integrand in regions which Lebesgue measure tends to zero when a parameter goes to zero. We will illustrate these abstract results through two applications, both in Lipschitz domains of R2, where we add a concentration term in semi linear elliptic problems: oscillating boundary domain which tends to a fixed limit domain; and a thin domain with a oscillatory boundary. In both cases we prove the upper and lower semicontinuity of the family of solutions from these problems.
 
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final.pdf (1.59 Mbytes)
Publishing Date
2017-12-06
 
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