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We prove the existence of a Radon measure-valued solution for a class of nonlinear degenerate parabolic equations with a “logarithmic diffusion” when the initial datum u 0 is a bounded Radon measure, and we study the regularity of these solutions. In particular, we prove that a regularizing effect appears if the initial datum is diffused with respect to the “ C 2 -capacity” since in this case the solution becomes a summable function. Finally, we study the uniqueness of these measure-valued solutions.
Journal of Evolution Equations – Springer Journals
Published: Sep 1, 2015
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