Results 81 to 90 of about 8,395 (199)

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

Annals of Mathematics, 2018
In this paper, we establish the global $C^{2,\alpha}$ and $W^{2,p}$ regularity for the Monge-Amp\`ere equation subject to a natural boundary condition arising in optimal transportation.
Shibing Chen, Jiakun Liu, Xu-jia Wang
semanticscholar   +1 more source

Soft Kirigami Composites for Form‐Finding of Fully Flexible Deployables

Advanced Materials Technologies, Volume 9, Issue 1, January 8, 2024.
A new class of thin flexible structures are introduced that morph from flat into prescribed 3D shapes without an external stimulus such as mechanical loads or heat. To achieve control over the target shape, two different concepts are coupled: strain mismatch (inspired by biological growth) and kirigami cuts.
Jan Zavodnik, Yunbo Wang, Wenzhong Yan, Miha Brojan, Mohammad Khalid Jawed   +4 more
wiley   +1 more source

Aleksandrov-type estimates for a parabolic Monge-Ampere equation

Electronic Journal of Differential Equations, 2005
A classical result of Aleksandrov allows us to estimate the size of a convex function $u$ at a point $x$ in a bounded domain $Omega$ in terms of the distance from $x$ to the boundary of $Omega$ if $$int_{Omega} det D^{2}u , dx less than infty ...
David Hartenstine
doaj  

Smooth approximation of twisted Kähler-Einstein metrics

Advanced Nonlinear Studies, 2023
In this article, we prove the existence of smooth approximations of twisted Kähler-Einstein metrics using the variational method.
Jin Lize, Wang Feng
doaj   +1 more source

The Monge–Ampère equation and its link to optimal transportation [PDF]

, 2013
We survey old and new regularity theory for the Monge-Ampere equation, show its connection to optimal transportation, and describe the regularity properties of a general class of Monge-Ampere type equations arising in that context.
G. Philippis, A. Figalli
semanticscholar   +1 more source

Comparison of two notions of subharmonicity on non-archimedean curves

, 2018
We show that a continuous function on the analytification of a smooth proper algebraic curve over a non-archimedean field is subharmonic in the sense of Thuillier if and only if it is psh, i.e. subharmonic in the sense of Chambert-Loir and Ducros.
Wanner, Veronika
core   +1 more source

Extended symmetry of the Witten-Dijkgraaf-Verlinde-Verlinde equation of Monge-Ampere type [PDF]

Opuscula Mathematica
We construct the Lie algebra of extended symmetry group for the Monge-Ampere type Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation. This algebra includes novel generators that are unobtainable within the framework of the classical Lie approach and ...
Patryk Sitko, Ivan Tsyfra
doaj   +1 more source

The hypersurfaces with conformal normal Gauss map in Hn+1 and S1n+1

Anais da Academia Brasileira de Ciências, 2008
In this paper, we introduce the fourth fundamental forms for hypersurfaces in Hn+1 and space-like hypersurfaces in S1n+1, and discuss the conformality of the normal Gauss map of the hypersurfaces in Hn+1 and S1n+1.
Shuguo Shi
doaj   +1 more source

A generalised comparison principle for the Monge-Amp\`ere equation and the pressure in 2D fluid flows

, 2016
We extend the generalised comparison principle for the Monge-Amp\`ere equation due to Rauch & Taylor (Rocky Mountain J. Math. 7, 1977) to nonconvex domains. From the generalised comparison principle we deduce bounds (from above and below) on solutions of
Ozanski, Wojciech
core  

Geophysical Monge–Ampère-Type Equation: Symmetries and Exact Solutions

Mathematics
This paper studies a mixed PDE containing the second time derivative and a quadratic nonlinearity of the Monge–Ampère type in two spatial variables, which is encountered in geophysical fluid dynamics.
Andrei D. Polyanin, Alexander V. Aksenov
doaj   +1 more source