 
Summary: Irreducibility of the transition semigroup
associated with the two phase Stefan problem
Viorel Barbu 1
University of Iasi, 6600 Iasi, Romania
Giuseppe Da Prato 2
Scuola Normale Superiore, 56126, Pisa, Italy
Abstract. 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].
2000 Mathematics Subject Classification AMS : 35K35, 35R15, 60H15.
Key words: Stochastic Stefan problem, invariant measures, transition semi
group, irreducibility.
1 Introduction
Let O be a bounded open domain of Rn
, n N, with a smooth boundary
O.
We are concerned with the following stochastic differential equation,
