On a class of elliptic operators with unbounded coefficients in convex domains
Giuseppe Da Prato, Alessandra Lunardi (2004)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We study the realization of the operator in , where is a possibly unbounded convex open set in , is a convex unbounded function such that and , is the element with minimal norm in the subdifferential of at , and is a probability measure, infinitesimally invariant for . We show that , with domain is a dissipative self-adjoint operator in . Note that the functions in the domain of do not satisfy any particular boundary condition. Log-Sobolev and Poincaré inequalities...