Pointwise estimates on derivatives of Coulombic wave functions and their electron densities

粗糙密度的最优传输映射的逐点Schauder估计

Pointwise Schauder estimates for optimal transport maps of rough densities

本文研究了粗糙密度下的最优传输问题，在密度仅于某$L^p$意义下接近常数的条件下，证明了最优传输映射势函数的逐点$C^{2,\,α}$估计。

$N$维Sierpinski垫片上能量密度的逐点正则性与不规则性

Pointwise regularity and irregularity of energy densities on $N$-dimensional Sierpinski gaskets

研究$N$维Sierpinski垫片上调和函数关于Kusuoka测度的能量密度的逐点正则性，证明非常值调和函数的每个Borel代表元在一个满Kusuoka测度集上每点不连续，而在每个一维边上存在规范逐点版本且具有显式最优Hölder指数。

Pointwise estimates for bipolar compressible Navier-Stokes-Poisson system in dimension three

The Cauchy problem of the bipolar Navier-Stokes-Poisson system (1.1) in dimension three is considered. We obtain the pointwise estimates of the time-asymptotic shape of the solution, which exhibit generalized Huygens' principle as the Navier-Stokes system. This phenomenon is the the most important difference from the unipolar Navier-Stokes-Poisson system. Due to non-conservative structure of the system (1.1) and interplay of two carriers which counteracts the influence of electric field (a nonlocal term), some new observations are essential for the proof. We make full use of the conservative s…

Pointwise space-time estimates of two-phase fluid model in dimension three

In this paper, we investigate the pointwise space-time behavior of two-phase fluid model derived by Choi \cite{Choi} [SIAM J. Math. Anal., 48(2016), pp. 3090-3122], which is the compressible damped Euler equations coupled with compressible Naiver-Stokes equations. Based on Green's function method together with frequency analysis and nonlinear coupling of different wave patterns, it shows that both of two densities and momentums obey the generalized Huygens' principle as the compressible Navier-Stokes equations \cite{LW}, however, it is different from the compressible damped Euler equations \ci…

Bounds for the gradient of the transition kernel for elliptic operators with unbounded diffusion, drift and potential term

We prove global Sobolev regularity and pointwise upper bounds for the gradient of transition densities associated with second order differential operators in $\mathbb{R}^d$ with unbounded diffusion, drift and potential terms.

Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials

We establish a priori upper bounds for solutions to the spatially inhomogeneous Landau equation in the case of moderately soft potentials, with arbitrary initial data, under the assumption that mass, energy and entropy densities stay under control. Our pointwise estimates decay polynomially in the velocity variable. We also show that if the initial data satisfies a Gaussian upper bound, this bound is propagated for all positive times.