A matrix differential Harnack estimate for a class of ultraparabolic equations (Q462308)

The author proves that if \(u\) is a positive solution of a suitable ultraparabolic equation and if \(u\) and its derivatives up to the second order are bounded then the difference \(H(\log u)-H(\log f)\) of the Hessian matrices of \(\log u\) and of \(\log f\) is non-negatively definite, where \(f\) is the fundamental solution of the ultraparabolic equation with pole at the origin \((0,0)\). This estimate starts from the seminal paper by Li and Yau and it extends a celebrated result due to Hamilton.