Potential Analysis

, Volume 5, Issue 6, pp 611–625

Invariance of closed convex sets and domination criteria for semigroups

  • El-Maati Ouhabaz

DOI: 10.1007/BF00275797

Cite this article as:
Ouhabaz, E. Potential Anal (1996) 5: 611. doi:10.1007/BF00275797


Let a and b be two positive continuous and closed sesquilinear forms on the Hilbert space H=L2(Ω, μ). Denote by T=T(t)t≧0and S=S(t)t≧0the 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|≦S(t)|f| for all t≧0 and fH. The method proposed uses ideas on invariance of closed convex sets of H under semigroups. Applications to elliptic operators and concrete examples are given.

Mathematics Subject Classifications (1991)


Key words

sesquilinear formsconvex setspositivity of semigroupsdomination

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • El-Maati Ouhabaz
    • 1
    • 2
  1. 1.SFB 288Technische Universität BerlinBerlinGermany
  2. 2.Max-Planck Arbeitsgruppe, FB MathematikUniversität PotsdamPotsdamGermany
  3. 3.Equipe d'Analyse et de Mathématique AppliquésUniversité de Marne-la-ValleéNoisy-le-GrandFrance