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.
Fractional fast diffusion with initial data a Radon measure
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abstract
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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Nonnegative solutions to nonlocal parabolic equations
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.