The paper analyzes a model in surface growth where the uniqueness of weak solutions seems to be out of reach. We prove existence of a weak martingale solution satisfying energy inequalities and having the Markov property. Furthermore, under nondegeneracy conditions on the noise, we establish that any such solution is strong Feller and has a unique invariant measure.

Markovianity and ergodicity for a surface growth PDE

Flandoli, Franco;
2009

Abstract

The paper analyzes a model in surface growth where the uniqueness of weak solutions seems to be out of reach. We prove existence of a weak martingale solution satisfying energy inequalities and having the Markov property. Furthermore, under nondegeneracy conditions on the noise, we establish that any such solution is strong Feller and has a unique invariant measure.
surface growth model; weak energy solutions; Markov solutions; strong Feller property; ergodicity
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/69143
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