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• W3019848648 abstract "Abstract We show how Hölder estimates for Feller semigroups can be used to obtain regularity results for solutions to the Poisson equation $$Af=g$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mrow><mml:mi>A</mml:mi><mml:mi>f</mml:mi><mml:mo>=</mml:mo><mml:mi>g</mml:mi></mml:mrow></mml:math> associated with the (extended) infinitesimal generator of a Feller process. The regularity of f is described in terms of Hölder–Zygmund spaces of variable order and, moreover, we establish Schauder estimates. Since Hölder estimates for Feller semigroups have been intensively studied in the last years, our results apply to a wide class of Feller processes, e.g. random time changes of Lévy processes and solutions to Lévy-driven stochastic differential equations. Most prominently, we establish Schauder estimates for the Poisson equation associated with the fractional Laplacian of variable order. As a by-product, we obtain new regularity estimates for semigroups associated with stable-like processes." @default.
• W3019848648 created "2020-05-01" @default.
• W3019848648 creator A5017418548 @default.
• W3019848648 date "2020-04-27" @default.
• W3019848648 modified "2023-09-28" @default.
• W3019848648 title "Schauder Estimates for Poisson Equations Associated with Non-local Feller Generators" @default.
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• W3019848648 doi "https://doi.org/10.1007/s10959-020-01008-x" @default.
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