A priori estimates for integro-differential operators with measurable kernels

By M. Kassmann. 2009

236 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5b293fdc8be2a844a7c9d80ffb1d29b191d3e21f

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Delaunay-type singular solutions for the fractional Yamabe problem (2015, background): “This kind of kernels corresponds to tempered stable process and they have been studied in [20] and [32], for instance.”
Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: A unified approach via fractional De Giorgi classes (2016, result): “When p = 2, the literature is richer: similar results have been obtained in [5, 37, 39, 40] and [59, 19, 20].”
The weak Harnack inequality for the Boltzmann equation without cut-off (2016, background): “THE WEAK HARNACK INEQUALITY FOR THE BOLTZMANN EQUATION WITHOUT CUT-OFF 9 is made in [44], [14], [41], [29] and [21].”
Regularity theory for parabolic nonlinear integral operators (2011, unknown): “Kassmann showed previously a similar result for the stationary case in a very interesting paper where he developed the corresponding Moser scheme [15].”
Boundary Harnack inequality for Markov processes with jumps (2012, unknown): “Related results have been recently studied when the Lévy kernel ν(x, y) is comparable to (d(x, y))−d−α (see [56] and the references therein).”
Regularity results for nonlocal parabolic equations (2013, background): “Several of the technical ingredients used in this work and in [28] are based on ideas in [36].”
The second eigenvalue of the fractional p-Laplacian (2014, methodology): “We recall that in the nonlocal setting, Moser’s iteration has already been employed in the linear case by Kassmann, in order to prove Hölder continuity for bounded solutions, see [18].”
Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation (2016, methodology): “More recently, the method has been extended to integral operators, such as fractional diﬀusion, in [10, 9] — see also the work of Kassmann [45] and of Kassmann and Felsinger [29].”
The Dirichlet Problem for the fractional p-Laplacian evolution equation (2015, background): “See the works [16, 37] for non-degenerate problems of this type, where C regularity of bounded solutions is proved.”
Regularity estimates for elliptic nonlocal operators (2015, methodology): “The next result is an extension of corresponding results in [20] and [2].”
Nonlocal elliptic equations in bounded domains: a survey (2015, methodology): “We refer to the reader to the following works on: • Existence of solutions: Felsinger-Kassmann-Voigt [25], Hoh-Jacob [31], and Barles-Imbert [3]; • Interior regularity of solutions: Bass-Levin [6], Kassmann [33], CaffarelliSilvestre [13, 14, 15], Barles-Chasseigne-Imbert [5], Kassmann-Mimica [34,…”