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A priori estimates for integro-differential operators with measurable kernels. (English) Zbl 1158.35019
Summary: The aim of this work is to develop a localization technique and to establish a regularity result for non-local integro-differential operators of order α(0,2). Thereby we extend the De Giorgi-Nash-Moser theory to non-local integro-differential operators. The operators under consideration generate strong Markov processes via the theory of Dirichlet forms. As is well known, regularity properties of the resolvents are important for many aspects of the corresponding stochastic process. Therefore, this work is related to probability theory and analysis, especially partial differential equations, at the same time.
MSC:
35D10Regularity of generalized solutions of PDE (MSC2000)
35B45A priori estimates for solutions of PDE
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35R05PDEs with discontinuous coefficients or data
47G20Integro-differential operators
60J75Jump processes
45K05Integro-partial differential equations
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