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Some classes of non-analytic Markov semigroups
Authors:G Metafune
Institution:a Dipartimento di Matematica “Ennio De Giorgi,” Università di Lecce, C.P. 193, 73100 Lecce, Italy
b Dipartimento di Matematica, Università di Torino, Italy
Abstract:We deal with Markov semigroups Tt corresponding to second order elliptic operators Au=Δu+〈Du,F〉, where F is an unbounded locally Lipschitz vector field on View the MathML source. We obtain new conditions on F under which Tt is not analytic in View the MathML source. In particular, we prove that the one-dimensional operator Au=u″−x3u′, with domain View the MathML source, View the MathML source, is not sectorial in View the MathML source. Under suitable hypotheses on the growth of F, we introduce a class of non-analytic Markov semigroups in View the MathML source, where μ is an invariant measure for Tt.
Keywords:
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