Removable Sets for Fractional Heat and Fractional Bessel-Heat Equations

Abstract

We examine the fractional heat diffusion equations $L_{\gamma ,a}:=(-{\Delta }_a{)}^{\frac{\gamma }{2}}+{\partial }_t$, where ${\Delta }_a$ is the Laplace- or the Bessel-Laplace operator. We give conditions for removability which are sufficient and which are necessary, by $L^p$-capacities. Introducing a spherical modulus of smoothness we can treat the Laplace and Bessel-Laplace cases together.

15 pages