Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach. [PDF]
Entropy (Basel), 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.
Islas C, Padilla P, Prado MA.
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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
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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, Ji-Guang Bao, Zixiao Liu
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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}$$C^
M. Sroka
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Stability and guaranteed error control of approximations to the Monge–Ampère equation [PDF]
Numerische Mathematik, 2023 This paper analyzes a regularization scheme of the Monge–Ampère equation by uniformly elliptic Hamilton–Jacobi–Bellman equations. The main tools are stability estimates in the $$L^\infty $$ L ∞ norm from the theory of viscosity solutions which are ...
D. Gallistl, Ngoc Tien Tran
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Trivariate Spline Collocation Methods for Numerical Solution to 3D Monge-Ampère Equation [PDF]
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
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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
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The Dirichlet problem for the Monge–Ampère equation on Hermitian manifolds with boundary [PDF]
Calculus of Variations and Partial Differential Equations, 2021 We study weak quasi-plurisubharmonic solutions to the Dirichlet problem for the complex Monge–Ampère equation on a general Hermitian manifold with non-empty boundary.
S. Kołodziej, N. Nguyen
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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
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Discrete Aleksandrov solutions of the Monge-Ampere equation
Electronic Journal of Differential Equations, 2022 We make two relaxations of the Oliker-Prussner method for the Dirichlet problem for the Monge-Ampere equation. First we relax the convexity requirement and consider mesh functions which are only discrete convex.
Gerard Awanou
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