# American Institute of Mathematical Sciences

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

 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.
Citation: Giuseppe Da Prato, Alessandra Lunardi. Maximal dissipativity of a class of elliptic degenerate operators in weighted $L^2$ spaces. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : 751-760. doi: 10.3934/dcdsb.2006.6.751
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