Results 41 to 50 of about 5,226,204 (223)

Solutions to the Monge–Ampère Equation with Polyhedral and Y-Shaped Singularities [PDF]

Journal of Geometric Analysis, 2020
We construct convex functions on R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin ...
Connor Mooney
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A new gradient estimate for the complex Monge–Ampère equation [PDF]

Mathematische Annalen, 2021
A gradient estimate for complex Monge–Ampère equations which improves in some respects on known estimates is proved using the ABP maximum principle.
B. Guo, Phong H. Duong, Freid Tong
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Solving the Dirichlet problem for the Monge-Ampère equation using neural networks [PDF]

Journal of Computational Mathematics and Data Science, 2021
The Monge-Amp\`ere equation is a fully nonlinear partial differential equation (PDE) of fundamental importance in analysis, geometry and in the applied sciences.
K. Nyström, Matias Vestberg
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Hölder continuous solutions of the Monge-Ampère equation on compact Hermitian manifolds [PDF]

, 2018
We show that a positive Borel measure of positive finite total mass, on a compact Hermitian manifold, admits a Hölder continuous quasi-plurisubharmonic solution to the Monge-Ampère equation if and only if it is dominated locally by Monge-Ampère measures ...
Nguyen, Ngoc Cuong, Kołodziej, Sławomir, Nguyen, Ngoc   +2 more
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On Neumann problem for the degenerate Monge–Ampère type equations

Boundary Value Problems, 2021
In this paper, we study the global C 1 , 1 $C^{1, 1}$ regularity for viscosity solution of the degenerate Monge–Ampère type equation det [ D 2 u − A ( x , D u ) ] = B ( x , u , D u ) $\det [D^{2}u-A(x, Du)]=B(x, u, Du)$ with the Neumann boundary value ...
Juhua Shi, Feida Jiang
doaj   +1 more source

Very weak solutions to the two-dimensional Monge-Ampére equation [PDF]

Science China Mathematics, 2019
In this short note we revisit the convex integration approach to constructing very weak solutions to the 2D Monge-Ampére equation with Hölder-continuous first derivatives of exponent β < 1/5. Our approach is based on combining the approach of Lewicka and
Wen-Tao Cao, L. Székelyhidi
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Interior C² estimate for monge-ampère equation in dimension two

, 2021
We obtain a genuine local C estimate for the Monge-Ampère equation in dimension two, by using the partial Legendre transform.
Jiakun Liu (14168568)
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Application of isotropic geometry to the solution of the Monge–Ampere equation

Қарағанды университетінің хабаршысы. Математика сериясы
This paper explores the Monge–Ampere equation in the context of isotropic geometry. The study begins with an overview of the fundamental properties of isotropic space, including its scalar product, distance formula, and the nature of surfaces and ...
Sh.Sh. Ismoilov
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Lie Group Classification, Symmetry Reductions, and Conservation Laws of a Monge-Ampère Equation

Symmetry
The nonhomogeneous Monge–Ampère equation, read as wxxwyy−wxy2+h(w)=0, is a nonlinear equation involving mixed second derivatives with respect to the spatial variables x and y, along with an additional source function h(w).
Samina Samina, Faiza Arif, Adil Jhangeer, Samad Wali   +3 more
semanticscholar   +1 more source

Boundedness of maximal function related to the Monge–Ampère equation

, 2007
In this paper, we establish the boundedness of maximal function on Morrey spaces related to the Monge–Ampère ...
Lin Tang, Xu, Jingshi, Tang, Lin, Jingshi Xu   +3 more
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