Michele de Oliveira Alves, Sergio Muniz Oliva
Abstract:
In this work we define the square root of the Laplacian operator with
Neumann boundary condition via harmonic extension method.
By using Fourier series and periodic even extension we define the
non-local operator square root in three type of bounded domains such
as an interval, square or a ball. Also, as application we study the
existence of weak solutions for a class of nonlinear elliptic problems.
Submitted June 17, 2013. Published January 8, 2014.
Math Subject Classifications: 35J50, 35S05.
Key Words: Harmonic extension; Neumann boundary condition;
square root of the Laplacian; nonlinear problem.
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Michele de Oliveira Alves Departamento de Matemática Universidade Estadual de Londrina Londrina, Brazil email: michelealves@uel.br | |
Sergio Muniz Oliva Departamento de Matemática Instituto de Matemática e Estatística Universidade de São Paulo São Paulo, Brazil email: smo@ime.usp.br |
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