Removable Lateral Singularities of Semilinear Parabolic PDEs and Besov Capacities

Suppose 1<α⩽2,Lis a second-order elliptic differential operator in RdandDis a bounded smooth domain in Rd. Let Q=R+×Dand letΓbe a compact set on the lateral boundary of Q. We prove thatΓis a removable lateral singularity for the equationu+Lu=uαin Q if and only if Cap1/α, 2/α, α′(Γ)=0 where Cap stands for the Besov capacity on the boundary.