Smooth measures and capacities associated with nonlocal parabolic operators

Abstract

We consider a family {L t , t ∈ [0, T ]} of closed operators generated by a family of regular (non-symmetric) Dirichlet forms {(. We apply this decomposition to the study of the structure of additive functionals in the Revuz correspondence with smooth measures. As a by-product, we also give some existence and uniqueness results for solutions of semilinear equations involving the operator ∂ ∂t + L t and a functional from the dual W ′ of the space W = {u ∈ L 2 (0, T ; V ) : ∂ t u ∈ L 2 (0, T ; V ′ )} on the right-hand side of the equation.Mathematics Subject Classification: Primary 31C25; Secondary 35K58, 31C15, 60J45.