Geodesic
Intrinsic scaling properties for nonlocal operators
Journal of the European Mathematical Society, Tome 19 (2017) no. 4, pp. 983-1011 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/686
Classification : 35-XX, 31-XX, 47-XX, 60-XX
Keywords: Integrodifferential operators, regularity, jump processes, intrinsic scaling 
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     author = {Moritz Kassmann and Ante Mimica},
     title = {Intrinsic scaling properties for nonlocal operators},
     journal = {Journal of the European Mathematical Society},
     pages = {983--1011},
     year = {2017},
     volume = {19},
     number = {4},
     doi = {10.4171/jems/686},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/686/}
}
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Moritz Kassmann; Ante Mimica. Intrinsic scaling properties for nonlocal operators. Journal of the European Mathematical Society, Tome 19 (2017) no. 4, pp. 983-1011. doi: 10.4171/jems/686

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