Caloric functions and boundary regularity for the fractional Laplacian
in Lipschitz open sets
Caloric functions and boundary regularity for the fractional Laplacian
in Lipschitz open sets
We give Martin representation of nonnegative functions caloric with respect to the fractional Laplacian in Lipschitz open sets. The caloric functions are defined in terms of the mean value property for the space-time isotropic $\alpha$-stable L\'evy process. To derive the representation, we first establish the existence of the parabolic Martin …