Local regularity for parabolic nonlocal operators

Details Local regularity for parabolic nonlocal operators Local regularity for parabolic nonlocal operators

2012-03-09

arxiv.org/abs/1203.2126v1

Mathematics

Analysis of PDEs

26 pages, 3 figures

Scientific paper

Weak solutions to parabolic integro-differential operators of order $\alpha
\in (\alpha_0, 2)$ are studied. Local a priori estimates of H\"older norms and
a weak Harnack inequality are proved. These results are robust with respect to
$\alpha \nearrow 2$. In this sense, the presentation is a generalization of
Moser's result in 1971.

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