Invariance of closed convex sets and domination criteria for semigroups

Let a and b be two positive continuous and closed sesquilinear forms on the Hilbert space H = L(2)(Omega, mu). Denote by T = T(t)(t greater than or equal to 0) and S = S(t)(t greater than or equal to 0), the semigroups generated by a and b on H. We give criteria in terms of a and b guaranteeing that the semigroup T is dominated by S, i.e. \T(t)f\ less than or equal to S(t)\f\ for all t greater than or equal to 0 and f is an element of H. The method proposed uses ideas on invariance of closed convex sets of H under semigroups. Applications to elliptic operators and concrete examples are given.