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July  2006, 6(4): 751-760. doi: 10.3934/dcdsb.2006.6.751

Maximal dissipativity of a class of elliptic degenerate operators in weighted $L^2$ spaces

Giuseppe Da Prato 1, and  Alessandra Lunardi 2,

1. 

Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126, Pisa, Italy
2. 

Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53, 43100 Parma, Italy

Received  March 2005 Revised  September 2005 Published  April 2006

We consider a degenerate elliptic Kolmogorov--type operator arising from second order stochastic differential equations in $\mathbb R^{n}$ perturbed by noise. We study a realization of such an operator in $L^2$ spaces with respect to an explicit invariant measure, and we prove that it is $m$-dissipative.
Keywords: Kolmogorov operators, Second order stochastic equations, invariant measures., degenerate elliptic operators.
Mathematics Subject Classification: 35J70, 60H10, 37L4.
Citation: Giuseppe Da Prato, Alessandra Lunardi. Maximal dissipativity of a class of elliptic degenerate operators in weighted $L^2$ spaces. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : 751-760. doi: 10.3934/dcdsb.2006.6.751
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