Um problema de extensão relacionado ao laplaciano fracionário e aplicações

Abstract

The Laplacian operator positivity allows its square roots de nition and this relates directly to the problem of harmonious extension in the superior semi-space, like an operator that takes the condition from Dirichlet's outline to the Neumann's condition. In this work, that was based on results developed by Ca areli and Silvestre [8], we got similar characterization for the Fractional Laplacian Operator. In addition, we apply the characterization reported to the sdudy of existence of non-trivial solution of the non-linear fractional Schrodinger equation.