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

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