Elliptic operators with unbounded drift coefficients and Neumann boundary condition |
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Authors: | Giuseppe Da Prato |
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Affiliation: | a Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy b Dipartimento di Matematica, Università di Parma, Via D'Azeglio 85/A, 43100 Parma, Italy |
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Abstract: | We study the realization AN of the operator in L2(Ω,μ) with Neumann boundary condition, where Ω is a possibly unbounded convex open set in , U is a convex unbounded function, DU(x) is the element with minimal norm in the subdifferential of U at x, and is a probability measure, infinitesimally invariant for . We show that AN is a dissipative self-adjoint operator in L2(Ω,μ). Log-Sobolev and Poincaré inequalities allow then to study smoothing properties and asymptotic behavior of the semigroup generated by AN. |
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Keywords: | |
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