Electron. J. Diff. Equ., Vol. 2014 (2014), No. 12, pp. 1-18.

An extension problem related to the square root of the Laplacian with Neumann boundary condition

Michele de Oliveira Alves, Sergio Muniz Oliva

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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