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Cores for generators of \(C_{0}\)-semigroups satisfying the Feller property

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Abstract

We deepen the study of the elliptic differential operator \(Au=\alpha u^{\prime \prime }+\beta u^{\prime }\) on (weighted) spaces of continuous functions on a real interval. We establish several sufficient conditions implying, at the same time, the generation of positive \(C_{0}\)-semigroups satisfying the Feller property and the existence of suitable cores. Some criteria on the regularity of the derivative, for functions satisfying Wentzell-type boundaries conditions, are also presented.

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Acknowledgments

The author wish to thank the anonymous referee for his/her accuracy in refereeing the paper and for his/her useful comments.

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  1. Dipartimento di Matematica, Università degli Studi di Bari “A. Moro”, Via E. Orabona, 4, 70125 , Bari, Italy

    Sabina Milella

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  1. Sabina Milella
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Correspondence to Sabina Milella.

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Communicated by Markus Haase.

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Milella, S. Cores for generators of \(C_{0}\)-semigroups satisfying the Feller property. Semigroup Forum 90, 317–338 (2015). https://doi.org/10.1007/s00233-014-9615-y

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