Let $\cal A$ be an elliptic operator with unbounded and sufficiently smooth coefficients and let $\mu$ be a (sub)-invariant measure of the operator $\cal A$. In this paper we give sufficient conditions guaranteeing that the closure of the operator $(\cal A, C^\infty_c(\R^N))$ generates a sub-Markovian strongly continuous semigroup of contractions in $L^p(\R^N,\mu)$. Applications are given in the case when $\cal A$ is a generalized Schrodinger operator.

L^p-uniqueness for elliptic operators with unbounded coefficients in R^N

ALBANESE, Angela Anna;MANGINO, Elisabetta Maria
2009-01-01

Abstract

Let $\cal A$ be an elliptic operator with unbounded and sufficiently smooth coefficients and let $\mu$ be a (sub)-invariant measure of the operator $\cal A$. In this paper we give sufficient conditions guaranteeing that the closure of the operator $(\cal A, C^\infty_c(\R^N))$ generates a sub-Markovian strongly continuous semigroup of contractions in $L^p(\R^N,\mu)$. Applications are given in the case when $\cal A$ is a generalized Schrodinger operator.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/327654
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