, Volume 19, Issue 1, pp 69-87

On Regularity for Beurling–Deny Type Dirichlet Forms

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Abstract

Characteristic examples of Beurling–Deny type Dirichlet forms are considered. The forms are identified with bilinear forms of integro-differential operators that arise as generators of jump-diffusion processes. The aim of this article is to prove Harnack inequalities for these operators and consequently Hölder regularity of weak H 1-solutions. Moser's iteration technique is used.