Results 31 to 40 of about 2,184 (136)

Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties [PDF]

, 2012
We show, using a direct variational approach, that the second boundary value problem for the Monge-Amp\`ere equation in R^n with exponential non-linearity and target a convex body P is solvable iff 0 is the barycenter of P.
Berman, Robert J., Berndtsson, Bo
core   +4 more sources

Generalized Liouville theorem for viscosity solutions to a singular Monge-Ampère equation

Advances in Nonlinear Analysis, 2023
In this article, we study the asymptotic behaviour at infinity for viscosity solutions to a singular Monge-Ampère equation in half space from affine geometry.
Jian Huaiyu, Wang Xianduo
doaj   +1 more source

Discretization of the 3D Monge-Ampere operator, between Wide Stencils and Power Diagrams [PDF]

, 2015
We introduce a monotone (degenerate elliptic) discretization of the Monge-Ampere operator, on domains discretized on cartesian grids. The scheme is consistent provided the solution hessian condition number is uniformly bounded.
Mirebeau, Jean-Marie
core   +3 more sources

Refined Boundary Behavior of the Unique Convex Solution to a Singular Dirichlet Problem for the Monge–Ampère Equation

Advanced Nonlinear Studies, 2018
This paper is concerned with the boundary behavior of the unique convex solution to a singular Dirichlet problem for the Monge–Ampère ...
Zhang Zhijun
doaj   +1 more source

Numerical solutions to two-dimensional fourth order parabolic thin film equations using the Parabolic Monge-Ampere method

AIMS Mathematics, 2023
This article presents the Parabolic-Monge-Ampere (PMA) method for numerical solutions of two-dimensional fourth-order parabolic thin film equations with constant flux boundary conditions.
Abdulghani R. Alharbi
doaj   +1 more source

On sharp lower bounds for Calabi type functionals and destabilizing properties of gradient flows

, 2020
Let $X$ be a compact K\"ahler manifold with a given ample line bundle $L$. In \cite{Don05}, Donaldson proved that the Calabi energy of a K\"ahler metric in $c_1(L)$ is bounded from below by the supremum of a normalized version of the minus Donaldson ...
Xia, Mingchen
core   +2 more sources

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, Khanh, Tran Vu, Pinton, Stefano   +2 more
core   +4 more sources

Nontrivial p-convex solutions to singular p-Monge-Ampère problems: Existence, Multiplicity and Nonexistence

Communications in Analysis and Mechanics
Our main objective of this paper is to study the singular $ p $-Monge-Ampère problems: equations and systems of equations. New multiplicity results of nontrivial $ p $-convex radial solutions to a single equation involving $ p $-Monge-Ampère operator are
Meiqiang Feng
doaj   +1 more source

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
doaj   +1 more source

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