REMOVABLE LATERAL SINGULARITIES OF SEMILINEAR PARABOLIC PDES AND BESOV CAPACITIES

Suppose 1 < alpha less than or equal to 2, L is a second-order ellipti c differential operator in R-d and D is a bounded smooth domain in R-d . Let 2 = R+ x D and let Gamma be a compact set on the lateral boundar y of 2. We prove that Gamma is a removable lateral singularity for the equation (u) over dot + Lu = u(alpha) in 2 if and only if Cap(1/alpha , 2/alpha, alpha')(Gamma) = 0 where Cap stands for the Besov capacity on the boundary. (C) 1998 Academic Press.