Abstract
We study regularity for a parabolic problem with fractional diffusion in space and a fractional time derivative. Our main result is a De Giorgi–Nash–Moser Hölder regularity theorem for solutions in a divergence form equation. We also prove results regarding existence, uniqueness, and higher regularity in time.
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Communicated by F. Lin
Mark Allen is supported by NSG Grant DMS-1303632. Luis Caffarelli is supported by NSF Grant DMS-1500871. Alexis Vasseur is supported by NSF Grant DMS-1209420.
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Allen, M., Caffarelli, L. & Vasseur, A. A Parabolic Problem with a Fractional Time Derivative. Arch Rational Mech Anal 221, 603–630 (2016). https://doi.org/10.1007/s00205-016-0969-z
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DOI: https://doi.org/10.1007/s00205-016-0969-z