Results 161 to 170 of about 8,395 (199)

Trivariate Spline Collocation Methods for Numerical Solution to 3D Monge-Ampère Equation

Journal of Scientific Computing, 2022
We use trivariate spline functions for the numerical solution of the Dirichlet problem of the 3D elliptic Monge-Ampére equation. Mainly we use the spline collocation method introduced in [SIAM J.
M. Lai, Jinsil Lee
semanticscholar   +1 more source

Solutions of the minimal surface equation and of the Monge–Ampère equation near infinity

Journal für die Reine und Angewandte Mathematik
Classical results assert that, under appropriate assumptions, solutions near infinity are asymptotic to linear functions for the minimal surface equation and to quadratic polynomials for the Monge–Ampère equation for dimension n ≥ 3 n\geq 3 , with an ...
Qing Han, Zhehui Wang
semanticscholar   +1 more source

Very weak solutions to the two-dimensional Monge-Ampére equation

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
Wentao Cao, L. Székelyhidi
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Quantitative Linearization Results for the Monge‐Ampère Equation

Communications on Pure and Applied Mathematics, 2019
This paper is about quantitative linearization results for the Monge‐Ampère equation with rough data. We develop a large‐scale regularity theory and prove that if a measure μ is close to the Lebesgue measure in Wasserstein distance at all scales, then ...
M. Goldman, M. Huesmann, F. Otto
semanticscholar   +1 more source

Moser-Trudinger inequalities and complex Monge-Ampère equation

ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2020
Our aim is to give a version of the Moser-Trudinger inequality in the setting of complex geometry. As a very particular case, our result already gives a new Moser-Trudinger inequality for functions in the Sobolev space $W^{1,2}$ of a domain in $R^2$.
T. Dinh, G. Marinescu, Duc-Viet Vu
semanticscholar   +1 more source

Blow-up solutions to the Monge–Ampère equation with a gradient term: sharp conditions for the existence and asymptotic estimates

Calculus of Variations and Partial Differential Equations, 2022
Xuemei Zhang, M. Feng
semanticscholar   +1 more source

Optimal boundary regularity for a singular Monge–Ampère equation

Journal of Differential Equations, 2018
In this paper we study the optimal global regularity for a singular Monge–Ampere type equation which arises from a few geometric problems. We find that the global regularity does not depend on the smoothness of domain, but it does depend on the convexity
H. Jian, You Li
semanticscholar   +1 more source

A recovery-based linear C0 finite element method for a fourth-order singularly perturbed Monge-Ampère equation

Advances in Computational Mathematics, 2021
Hongtao Chen, Xiaobing H. Feng, Zhimin Zhang   +2 more
semanticscholar   +1 more source

On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*

, 1978
S. Yau
semanticscholar   +1 more source

The Monge-ampere Equation and Its Applications

, 2017
A. Figalli
semanticscholar   +1 more source