Approximation of diffuse measures for parabolic capacities

Petitta, Francesco [] Porretta, Alessio [] Ponce, Augusto [UCL]

Given a parabolic cylinder Q = (0, T) x Omega, with Omega subset of R-N, we consider the class of finite measures which do not charge sets of zero p-parabolic capacity in Q. We prove that such measures can be strongly approximated by measures which can be written as v(t) - Delta(p)v with v is an element of L-p(0, T; W-0(1,p) (Omega)) boolean AND L-infinity (Q). Estimates on the capacity of level sets of solutions of parabolic equations play a crucial role in our proof.