Annali di Matematica Pura ed Applicata, 2021 In this paper, we establish a local regularity result for Wloc2,p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\
Soufian Abja, Guillaume Olive
semanticscholar +1 more source
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
Minimal convex extensions and finite difference discretization of the quadratic Monge-Kantorovich problem [PDF]
, 2018 We present an adaptation of the MA-LBR scheme to the Monge-Amp{\`e}re equation with second boundary value condition, provided the target is a convex set.
Benamou, Jean-David, Duval, Vincent
core +5 more sources
Continuous and Lp estimates for the complex Monge-Ampère equation on bounded domains in ℂn
International Journal of Mathematics and Mathematical Sciences, 2002 Continuous solutions with continuous data and Lp solutions with Lp data are obtained for the complex Monge-Ampère equation on bounded domains, without requiring any smoothness of the domains.
Patrick W. Darko
doaj +1 more source
Optimal global and boundary asymptotic behavior of large solutions to the Monge-Ampère equation
, 2020 This paper is mainly concerned with optimal global and boundary asymptotic behavior of strict convex large solutions to the Monge-Ampere equation det D 2 u = b ( x ) f ( u ) , x ∈ Ω , where Ω is a strict convex and bounded smooth domain in R n with n ≥ 2
Zhijun Zhang
semanticscholar +1 more source
Application of isotropic geometry to the solution of the Monge–Ampere equation
Қарағанды университетінің хабаршысы. Математика сериясыThis 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
doaj +1 more source
A curvature flow to the Lp Minkowski-type problem of q-capacity
Advanced Nonlinear Studies, 2023 This article concerns the Lp{L}_{p} Minkowski problem for q-capacity.
Liu Xinying, Sheng Weimin
doaj +1 more source
EURECOM:Monthly Bulletin of European Community Economic and Financial News. January 1999 Vol. 11, No. 1 [PDF]
, 1999 We show here a weak Hölder regularity up to the boundary of the solution to the Dirichlet problem for the complex Monge-Ampère equation with data in the Lp space and Ω satisfying an f-property.
Baracco, Luca +2 more
core +4 more sources
Moser-Trudinger inequality for the complex Monge-Ampère equation [PDF]
Journal of Functional Analysis, 2020 In this paper, we prove a Moser-Trudinger type inequality for pluri-subharmonic functions vanishing on the boundary. Our proof uses a descent gradient flow for the complex Monge-Ampere functional.
Jiaxiang Wang, Xu-jia Wang, Bin Zhou
semanticscholar +1 more source
Simplified Geometric Approach to Freeform Beam Shaper Design
International Journal of Optics, 2020 Beam of light shaping process can be considered ultimate, if both irradiance and wavefront spatial distributions are under control and both can be shaped arbitrarily.
Jacek Wojtanowski, Tadeusz Drozd
doaj +1 more source