On removable lateral singularities for quasilinear parabolic PDE's

Abstract

Suppose that L is a second order parabolic differential operator with smooth coefficients in a bounded smooth domain D and let Q T = [ 0 , T ] × D = [0, T] × D. Let 1 < α ≤ 2, and let Γ be a compact subset of the lateral boundary ∂ ∂ Q of Q T . We show that the following four properties are equivalent: o (a) Γ is a removable lateral singularity for the equation K + Lu = u α in Q T ; (b) The Poisson capacity of Γ is equal to zero; (c) The Besov capacity, Cap 1/α,2/α,α′(Γ), is equal to 0; (d) Γ is not hit by the graph of the ( L,α)-superdiffusion in Q T