Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations

We investigate stable solutions of elliptic equations of the type {(-Delta)(s) u = lambda f(u) in B-1 subset of R-n u = 0 on partial derivative B-1, where n >= 2, s is an element of (0, 1), lambda = 0 and f is any smooth positive superlinear function. The operator (-Delta)(s) stands for the fractional Laplacian, a pseudo- differential operator of order 2s. According to the value of lambda, we study the existence and regularity of weak solutions u.