arXiv subjects
Publications and source records attributed to Xinhang Tong.
In this paper we revisit the remainder terms of $L^p$-Hardy inequalities for magnetic $p$-Laplacians. In particular, we will give an integral representation of the sharp constant for a crucial algebraic inequality established by C. Cazacu, D. Krejčiřík, N. Lam, and A. Laptev.
We propose a simple proof of the exponential convergence to equilibrium for ultrafast diffusion equations in $\mathbb{R}^n$. Our approach, based on the direct use of Poincaré inequality, gets rid of the optimal transport arguments used in \cite{fathi2025} which are valid for Gaussian-excluded one-dimensional weights. This simplification allows us to extend their results to Gaussian measures in higher dimensions.
We study Hamamoto's expanding square argument towards a 1-D minimisation problem related to the sharp solenoidal uncertainty principle. Working in the right function space, we recast the involved interpolation type inequality into an exact equality, where the vanishing of the remainder term characterises the extremisers via the confluent hypergeometric functions. In the process we also remove some unnecessary constraints on the prescribed parameters.
We propose an $f$-divergence extension of the Hasegawa-Nishiyama thermodynamic uncertainty relation. More precisely, we introduce the stochastic thermodynamic entropy production based on generalised $f$-divergences and derive corresponding uncertainty relations in connection with the symmetry entropy.