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Regularity theory for singular nonlocal diffusion equations

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Abstract

We prove continuity for bounded weak solutions of a nonlinear nonlocal parabolic type equation associated to a Dirichlet form with a rough kernel. The equation is allowed to be singular at the level zero, and solutions may change sign. If the nonlinearity in the equation does not oscillate too much at the origin, the solution is proved to be moreover Hölder continuous. The results are new even when the Dirichlet form is the one corresponding to the fractional Laplacian.

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Acknowledgements

All authors supported by the Spanish Project MTM2014-53037-P.

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Correspondence to Fernando Quirós.

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Communicated by O. Savin.

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de Pablo, A., Quirós, F. & Rodríguez, A. Regularity theory for singular nonlocal diffusion equations. Calc. Var. 57, 136 (2018). https://doi.org/10.1007/s00526-018-1410-2

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  • DOI: https://doi.org/10.1007/s00526-018-1410-2

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