Spatial regularity of semigroups generated by Lévy type operators

Mingjie Liang and Jian Wang

Mathematische Nachrichten, 2019, vol. 292, issue 7, 1551-1566

Abstract: We apply the probabilistic coupling approach to establish spatial regularity of semigroups associated with Lévy type operators, by assuming that the corresponding martingale problem is well posed. In particular, we can prove the Lipschitz continuity of the associated semigroups, when the coefficients are Hölder continuous but the corresponding Lévy kernel may be singular.

Date: 2019
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