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.
Autori interni: | |
Autori: | Blömker, D; Flandoli, Franco; Romito, Marco |
Titolo: | Markovianity and ergodicity for a surface growth PDE |
Anno del prodotto: | 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. |
Digital Object Identifier (DOI): | 10.1214/08-AOP403 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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