Schauder Estimates for Equations Associated with Lévy Generators View Full Text


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Article Info

DATE

2019-04

AUTHORS

Franziska Kühn

ABSTRACT

We study the regularity of solutions to the integro-differential equation Af-λf=g associated with the infinitesimal generator A of a Lévy process. We show that gradient estimates for the transition density can be used to derive Schauder estimates for f. Our main result allows us to establish Schauder estimates for a wide class of Lévy generators, including generators of stable Lévy processes and subordinated Brownian motions. Moreover, we obtain new insights on the (domain of the) infinitesimal generator of a Lévy process whose characteristic exponent ψ satisfies Reψ(ξ)≍|ξ|α for large |ξ|. We discuss the optimality of our results by studying in detail the domain of the infinitesimal generator of the Cauchy process. More... »

PAGES

10

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00020-019-2508-4

DOI

http://dx.doi.org/10.1007/s00020-019-2508-4

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https://app.dimensions.ai/details/publication/pub.1112457133


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