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Hölder regularity for nondivergence nonlocal parabolic equations

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Abstract

This paper proves Hölder continuity of viscosity solutions to certain nonlocal parabolic equations that involve a generalized fractional time derivative of Marchaud or Caputo type. As a necessary and preliminary result, this paper first proves Hölder continuity for viscosity solutions to certain nonlinear ordinary differential equations involving the generalized fractional time derivative.

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Correspondence to Mark Allen.

Additional information

Communicated by L. Ambrosio.

M. Allen was supported by NSF Grant DMS-1303632.

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Allen, M. Hölder regularity for nondivergence nonlocal parabolic equations. Calc. Var. 57, 110 (2018). https://doi.org/10.1007/s00526-018-1367-1

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  • DOI: https://doi.org/10.1007/s00526-018-1367-1

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