Jiakun Liu

activity

20182026

most citedGlobal regularity for the Monge-Ampère equation with natural boundary condition

10 citations · 26 across the 9 of their papers we have counts for

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3 papers · 1 filter

math.AP2018★ 5 cited

$L_{p}$ -Brunn-Minkowski inequality for $p \in (1 - \frac{c}{n ^{\frac{3}{2}}}, 1)$

Shibing Chen, Yong Huang, Qi-rui Li +1

Kolesnikov-Milman [9] established a local $L_{p}$ -Brunn-Minkowski inequality for $p \in (1 - c / n^{\frac{3}{2}}, 1) .$ Based on their local uniqueness results for the $L_{p}$ -Minkowski proble…

math.AP2018★ 8 cited

Boundary regularity for the second boundary-value problem of Monge-Ampère equations in dimension two

Shibing Chen, Jiakun Liu, Xu-Jia Wang

In this paper, we introduce an iteration argument to prove that a convex solution to the Monge-Ampère equation $\mbox{det } D^2 u =f $ in dimension two subject to the natural bound…

math.AP2018★ 10 cited

Global regularity for the Monge-Ampère equation with natural boundary condition

Shibing Chen, Jiakun Liu, Xu-Jia Wang

In this paper, we establish the global $C^{2, α}$ and $W^{2, p}$ regularity for the Monge-Ampère equation $det D^{2} u = f$ subject to boundary condition $D u (Ω) = Ω^{*}$ , where $Ω$ and…

Lp​-Brunn-Minkowski inequality for p∈(1−n23​c​,1)

Boundary regularity for the second boundary-value problem of Monge-Ampère equations in dimension two

Global regularity for the Monge-Ampère equation with natural boundary condition

$L_{p}$ -Brunn-Minkowski inequality for $p \in (1 - \frac{c}{n ^{\frac{3}{2}}}, 1)$