<Emphasis Type="Italic">m</Emphasis>-Dissipativity of Some Gradient Systems with Measurable Potential |
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Authors: | Roberta Tognari |
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Institution: | (1) Dipartimento di Matematica, Universita di Pisa, Largo Bruno, Pontecorvo, 5, 56127 Pisa, Italy |
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Abstract: | We consider the operator in L
2(B, ν) and in L
1(B, ν) with Neumann boundary condition, where U is an unbounded function belonging to for some q ∈(1, ∞), B is the possibly unbounded convex open set in where U is finite and ν(dx) = C exp (−2U (x))dx is a probability measure, infinitesimally invariant for N
0. We prove that the closure of N
0 is a m-dissipative operator both in L
2(B, ν) and in L
1(B, ν). Moreover we study the properties of ergodicity and strong mixing of the measure ν in the L
2 case.
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Keywords: | Kolmogorov operators invariant measures m-dissipativity |
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