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- W2952941844 abstract "Let $u$ be a positive solution of the ultraparabolic equation begin{equation*} partial_t u=sum_{i=1}^n partial_{x_i}^2 u+sum_{i=1}^k x_ipartial_{x_{n+i}}u hspace{8mm} mbox{on} hspace{4mm} mathbb{R}^{n+k}times (0,T), end{equation*} where $1leq kleq n$ and $0<T leq +infty$. Assume that $u$ and its derivatives (w.r.t. the space variables) up to the second order are bounded on any compact subinterval of $(0,T)$. Then the difference $H(log u)- H(log f)$ of the Hessian matrices of $log u$ and of $log f$ (both w.r.t. the space variables) is non-negatively definite, where $f$ is the fundamental solution of the above equation with pole at the origin $(0,0)$. The estimate in the case $n=k=1$ is due to Hamilton. As a corollary we get that $Delta l+frac{n+3k}{2t}+frac{6k}{t^3}geq 0$, where $l=log u$, and $Delta=sum_{i=1}^{n+k} partial_{x_i}^2 $." @default.
- W2952941844 created "2019-06-27" @default.
- W2952941844 creator A5058819361 @default.
- W2952941844 date "2013-06-20" @default.
- W2952941844 modified "2023-10-16" @default.
- W2952941844 title "A matrix differential Harnack estimate for a class of ultraparabolic equations" @default.
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- W2952941844 doi "https://doi.org/10.48550/arxiv.1306.4810" @default.
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