Local regularity for parabolic nonlocal operators

Abstract

Weak solutions to parabolic integro-differential operators of order $\alpha \in ({\alpha }_0,2)$ are studied. Local a priori estimates of Hölder norms and a weak Harnack inequality are proved. These results are robust with respect to $\alpha \nearrow 2$. In this sense, the presentation is an extension of Moser's result in 1971.

31 pages, 3 figures

References in corpus (3)

• Regularity estimates for elliptic nonlocal operators
• Comparability and regularity estimates for symmetric nonlocal Dirichlet forms
• A weak Harnack inequality for fractional evolution equations with discontinuous coefficients

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