Convergent semi-Lagrangian methods for the Monge-Ampère equation on unstructured grids [PDF]
SIAM Journal on Numerical Analysis, 2017 This paper is concerned with developing and analyzing convergent semi-Lagrangian methods for the fully nonlinear elliptic Monge-Ampère equation on general triangular grids.
Barles G. +3 more
core +5 more sources
Boundary blow-up solutions to the Monge-Ampère equation: Sharp conditions and asymptotic behavior
Advances in Nonlinear Analysis, 2019 Consider the boundary blow-up Monge-Ampère ...
Zhang Xuemei, Feng Meiqiang
doaj +4 more sources
Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach [PDF]
Entropy, 2020 We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework.
Carlos Islas +2 more
doaj +2 more sources
Pluricomplex Green's functions and Fano manifolds [PDF]
Épijournal de Géométrie Algébrique, 2019 We show that if a Fano manifold does not admit Kahler-Einstein metrics then the Kahler potentials along the continuity method subconverge to a function with analytic singularities along a subvariety which solves the homogeneous complex Monge-Ampere ...
Nicholas McCleerey, Valentino Tosatti
doaj +3 more sources
Stability and guaranteed error control of approximations to the Monge–Ampère equation [PDF]
Numerische Mathematik, 2023 This paper analyzes a regularization scheme of the Monge–Ampère equation by uniformly elliptic Hamilton–Jacobi–Bellman equations. The main tools are stability estimates in the $$L^\infty $$ L ∞ norm from the theory of viscosity solutions which are ...
D. Gallistl, Ngoc Tien Tran
semanticscholar +1 more source
Sharp uniform bound for the quaternionic Monge-Ampère equation on hyperhermitian manifolds [PDF]
Calculus of Variations and Partial Differential Equations, 2022 We provide the sharp C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^
Marcin Sroka
semanticscholar +1 more source
Convergence of a regularized finite element discretization of the two-dimensional Monge-Ampère equation [PDF]
Mathematics of Computation, 2021 This paper proposes a regularization of the Monge–Ampère equation in planar convex domains through uniformly elliptic Hamilton–Jacobi–Bellman equations.
D. Gallistl, Ngoc Tien Tran
semanticscholar +1 more source
Entire solutions to the parabolic Monge–Ampère equation with unbounded nonlinear growth in time [PDF]
Nonlinear Analysis, 2023 The Liouville type theorem on the parabolic Monge--Amp\`ere equation $-u_t\det D^2u=1$ states that any entire parabolically convex classical solution must be of form $-t+|x|^2/2$ up to a re-scaling and transformation, under additional assumption that ...
Ning An, J. Bao, Zixiao Liu
semanticscholar +1 more source
Computing Three-Dimensional Freeform Reflectors with a Scattering Surface [PDF]
EPJ Web of Conferences, 2023 We present a novel approach to computing reflectors with a scattering surface in illumination optics. A scattering model governed by a Fredholm integral equation is derived.
Kronberg Vì C.E. +3 more
doaj +1 more source
Advanced Nonlinear Studies, 2023 We consider the asymptotic behavior of solutions to the Monge-Ampère equations with slow convergence rate at infinity and fulfill previous results under faster convergence rate by Bao et al. [Monge-Ampère equation on exterior domains, Calc. Var PDE.
Liu Zixiao, Bao Jiguang
doaj +1 more source