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• W3009188863 abstract "We establish the interior and boundary Holder continuity of possibly sign-changing solutions to a class of doubly nonlinear parabolic equations whose prototype is [ partial_tbig(|u|^{p-2}ubig)-Delta_p u=0,quad p>1. ] The proof relies on the property of expansion of positivity and the method of intrinsic scaling, all of which are realized by De Giorgi's iteration. Our approach, while emphasizing the distinct roles of sub(super)-solutions, is flexible enough to obtain the Holder regularity of solutions to initial-boundary value problems of Dirichlet type or Neumann type in a cylindrical domain, up to the parabolic boundary. In addition, based on the expansion of positivity, we are able to give an alternative proof of Harnack's inequality for non-negative solutions. Moreover, as a consequence of the interior estimates, we also obtain a Liouville-type result." @default.
• W3009188863 created "2020-03-13" @default.
• W3009188863 creator A5024466207 @default.
• W3009188863 creator A5032210771 @default.
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• W3009188863 date "2020-03-09" @default.
• W3009188863 modified "2023-10-14" @default.
• W3009188863 title "On the Holder regularity of signed solutions to a doubly nonlinear equation" @default.
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• W3009188863 doi "https://doi.org/10.48550/arxiv.2003.04158" @default.
• W3009188863 hasPublicationYear "2020" @default.
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