Zobrazeno 1 - 10
of 185
pro vyhledávání: '"Chen Shibing"'
In this paper, we investigate the optimal (partial) transport problems when the target is a non-convex polygonal domain in \(\mathbb{R}^2\). For the complete optimal transportation, we prove that the singular set is locally a 1-dimensional smooth cur
Externí odkaz:
http://arxiv.org/abs/2311.15655
In this paper, we establish the global $W^{2,p}$ estimate for the Monge-Amp\`ere obstacle problem: $(Du)_{\sharp}f\chi{_{\{u>\frac{1}{2}|x|^2\}}}=g$, where $f$ and $g$ are positive continuous functions supported in disjoint bounded $C^2$ uniformly co
Externí odkaz:
http://arxiv.org/abs/2307.00262
The current work focuses on the Gaussian-Minkowski problem in dimension 2. In particular, we show that if the Gaussian surface area measure is proportional to the spherical Lebesgue measure, then the corresponding convex body has to be a centered dis
Externí odkaz:
http://arxiv.org/abs/2303.17389
Autor:
Chen, Shibing, Liu, Jiakun
In this work, we develop a regularity theory for the optimal transport problem when the target consists of two disjoint convex domains, a fundamental model in which singularities of optimal transport maps arise. When the target is partitioned into tw
Externí odkaz:
http://arxiv.org/abs/2210.13841
In this note, we prove the uniqueness of blowups at singular points of the no-sign obstacle problem $\Delta u=\chi_{_{B_1\backslash \{u=|Du|=0\}}}\ \text{in}\ B_1,$ thus give a positive answer to a problem raised in \cite[Notes of Chaper 7, page 149]
Externí odkaz:
http://arxiv.org/abs/2204.11426
In this paper, we prove the uniqueness of solutions to the logarithmic Minkowski problem in $\mathbb{R}^3$ without symmetry condition, provided the density of the measure is close to $1$ in $C^{\alpha}$ norm. This result also implies the uniqueness o
Externí odkaz:
http://arxiv.org/abs/2202.10074
We prove that a hemisphere in the Euclidean space $R^{n+1}$, viewed as the graph of a function, admits no smooth perturbations as graphs with mean curvature $H\ge 1$ whose boundary equator is fixed up to $C^2$. This is an extension of the \emph{Mean
Externí odkaz:
http://arxiv.org/abs/2202.09824
Publikováno v:
In Journal of Differential Equations 25 August 2024 401:671-682
Publikováno v:
Advanced Nonlinear Studies, Vol 23, Iss 1, Pp 375-417 (2023)
In this note, we establish the global C3,α{C}^{3,\alpha } regularity for potential functions in optimal transportation between hypercubes in Rn{{\mathbb{R}}}^{n} for n≥3n\ge 3. When n=2n=2, the result was proved by Jhaveri. The C3,α{C}^{3,\alpha
Externí odkaz:
https://doaj.org/article/f51ed278e7834ae1b5350933cd2acf35
Publikováno v:
In Journal of Molecular Liquids 1 December 2023 391 Part A