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arXiv · 1903.07843

Global regularity for degenerate/singular parabolic equations involving measure data

Sun-Sig Byun·Jung-Tae Park·Pilsoo Shin
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Abstract

We consider degenerate and singular parabolic equations with $p$-Laplacian structure in bounded nonsmooth domains when the right-hand side is a signed Radon measure with finite total mass. We develop a new tool that allows global regularity estimates for the spatial gradient of solutions to such parabolic measure data problems, by introducing the (intrinsic) fractional maximal function of a given measure.

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Sun-Sig Byun, Jung-Tae Park, Pilsoo Shin. 2019-03-19. Global regularity for degenerate/singular parabolic equations involving measure data. https://doi.org/10.1007/s00526-020-01906-2

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