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- W4376654048 abstract "This paper is devoted to studying the local behavior of non-negative weak solutions to the doubly non-linear parabolic equation begin{equation*} partial_t u^q - text{div}big(|D u|^{p-2}D ubig) = 0 end{equation*} in a space-time cylinder. Holder estimates are established for the gradient of its weak solutions in the super-critical fast diffusion regime $0<p-1< q<frac{N(p-1)}{(N-p)_+}$ where $N$ is the space dimension. Moreover, decay estimates are obtained for weak solutions and their gradient in the vicinity of possible extinction time. Two main components towards these regularity estimates are a time-insensitive Harnack inequality that is particular about this regime, and Schauder estimates for the parabolic $p$-Laplace equation." @default.
- W4376654048 created "2023-05-17" @default.
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- W4376654048 date "2023-05-15" @default.
- W4376654048 modified "2023-09-29" @default.
- W4376654048 title "Holder Continuity of the Gradient of Solutions to Doubly Non-Linear Parabolic Equations" @default.
- W4376654048 doi "https://doi.org/10.48550/arxiv.2305.08539" @default.
- W4376654048 hasPublicationYear "2023" @default.
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