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Fractional fast diffusion with initial data a Radon measure

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arxiv 2503.14296 v2 pith:YRZPS2Y6 submitted 2025-03-18 math.AP

Jorge Ruiz-Cases This is my paper · ORCID
classification math.AP
keywords initialsolutionsdatadiffusionfastfractionalmeasureprove
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We establish a complete Widder Theory for the fractional fast diffusion equation. Our work focuses on nonnegative solutions satisfying a certain integral size condition at infinity. We prove that these solutions possess a Radon measure as initial trace, and prove the existence and uniqueness of solutions originating from such initial data. The uniqueness result is the main issue. Most of its difficulty comes from the singular character of the nonlinearity.

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  1. Nonnegative solutions to nonlocal parabolic equations

    math.AP 2025-05 conditional novelty 8.0 of 10

    Nonnegative solutions to nonlocal parabolic equations with bounded measurable coefficients are represented exactly by a fundamental solution, with sharp two-sided bounds and new Harnack inequalities.

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