Irreducibility of the Transition Semigroup Associated with the Two Phase Stefan Problem

  • Viorel Barbu
  • Giuseppe Da Prato
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 79)


We prove that the transition semigroup associated with the two phase Stefan problem is irreducible. The proof relies on a general result of approximate controllability for maximal monotone systems, see [1].

Key words

Stochastic Stefan problem invariant measures transition semigroup irreducibility 


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  1. [1]
    V. Barbu, “Analysis and control of nonlinear infinite dimensional systems”, Academic Press, San Diego, 1993.zbMATHGoogle Scholar
  2. [2]
    V. Barbu and G. Da Prato, “The two phase stochastic Stefan problem”, Probab. Theory Relat. Fields, 124, 544–560, 2002.zbMATHCrossRefGoogle Scholar
  3. [3]
    H. Brézis, “Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations”, Contributions to Nonlinear Functional Analysis, E. Zarantonello, ed., Academic Press, New York, 1971.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Viorel Barbu
    • 1
  • Giuseppe Da Prato
    • 2
  1. 1.University of IasiIasiRomania
  2. 2.Scuola Normale SuperiorePisaItaly

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