The heat equation for the Dirichlet fractional Laplacian with Hardy's potentials: properties of minimal solutions and blow-up

Abstract

Local and global properties of minimal solutions for the heat equation generated by the Dirichlet fractional Laplacian negatively perturbed by Hardy's potentials on open subsets of $\R^d$ are analyzed. As a byproduct we obtain instantaneous blow-up of nonnegative solutions in the supercritical case.