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Doctoral Thesis
DOI
10.11606/T.45.2010.tde-19012011-231320
Document
Author
Full name
Michele de Oliveira Alves
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2010
Supervisor
Committee
Oliva Filho, Sergio Muniz (President)
Táboas, Plácido Zoega
Lopes, Orlando Francisco
Soares, Sérgio Henrique Monari
Terra, Joana Isabel Afonso Mourão
Title in Portuguese
Um problema de extensão relacionado a raiz quadrada do Laplaciano com condição de fronteira de Neumann
Keywords in Portuguese
condições de fronteira de Neumann
extensão harmônica
operador não local
problemas não lineares
raiz quadrada do Laplaciano
série de Fourier
Abstract in Portuguese
Neste trabalho definimos o operador não local, raiz quadrada do Laplaciano com condição de fronteira de Neumann, através do método de extensão harmônica. O estudo foi feito com o auxílio das séries de Fourier em domínios limitados, como sendo o intervalo, o quadrado e a bola. Posteriormente, aplicamos nosso estudo, à problemas elípticos não lineares envolvendo o operador não local raiz quadrada do Laplaciano com condição de fronteira de Neumann.
Title in English
An extension problem related to the square root of the Laplacian with Neumann boundary condition
Keywords in English
Fourier series
harmonic extension
Neumann boundary conditions
non-local operator
nonlinear problems
square root of the Laplacian
Abstract in English
In this work we define the non-local operator, square root of the Laplacian with Neumann boundary condition, using the method of harmonic extension. The study was done with the aid of Fourier series in bounded domains, as the interval, the square and the ball. Subsequently, we apply our study, the nonlinear elliptic problems involving non-local operator square root of the Laplacian with Neumann boundary condition.
 
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preambulo.pdf (569.25 Kbytes)
Publishing Date
2011-05-12
 
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