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Regularity theory for parabolic nonlinear integral operators. (English) Zbl 1223.35098
The authors consider nonlocal evolution equations of variational type with measurable and symmetric kernels. Similar equations were conisidered by Kassmann and Barlow, Bass, Chen and Kassmann. Those authors proved that a Harnack inequality holds also in a very general case, but in general the solution is not Hölder continuous. In this paper, thanks to the assumption of the symmetry of the kernel, the authors are able to prove the Hölder continuity of the solution by applying the classical de Giorgi method in a smart way. This equation is motivated by several applications in image and signal processing.

MSC:
35B65 Smoothness and regularity of solutions to PDEs
35R09 Integral partial differential equations
45G05 Singular nonlinear integral equations
47G10 Integral operators
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