JournalsjemsVol. 19, No. 4pp. 983–1011

Intrinsic scaling properties for nonlocal operators

  • Moritz Kassmann

    Universität Bielefeld, Germany
  • Ante Mimica

    University of Zagreb, Croatia
Intrinsic scaling properties for nonlocal operators cover
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Abstract

We study integrodifferential operators and regularity estimates for solutions to integrodifferential equations. Our emphasis is on kernels with a critically low singularity which does not allow for standard scaling. For example, we treat operators that have a logarithmic order of differentiability. For corresponding equations we prove a growth lemma and derive a priori estimates. We derive these estimates by classical methods developed for partial differential operators. Since the integrodifferential operators under consideration generate Markov jump processes, we are able to offer an alternative approach using probabilistic techniques.

Cite this article

Moritz Kassmann, Ante Mimica, Intrinsic scaling properties for nonlocal operators. J. Eur. Math. Soc. 19 (2017), no. 4, pp. 983–1011

DOI 10.4171/JEMS/686