Results 21 to 30 of about 188 (177)

The first initial-boundary value problem of parabolic Monge–Ampère equations outside a bowl-shaped domain

Boundary Value Problems, 2021
In this paper, we study the parabolic Monge–Ampère equations − u t det ( D 2 u ) = g $-u_{t}\det (D^{2}u)=g$ outside a bowl-shaped domain with g being the perturbation of g 0 ( | x | ) $g_{0}(|x|)$ at infinity.
Limei Dai, Huihui Cheng
doaj   +1 more source

The Maximal Regularity of Nonlocal Parabolic Monge–Ampère Equations and Its Monotonicity in the Whole Space

Axioms
The Monge–Ampère operator, as a nonlinear operator embedded in parabolic differential equations, complicates the demonstration of maximal regularity for these equations.
Xingyu Liu
doaj   +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

The Dirichlet Problem of Hessian Equation in Exterior Domains

Mathematics, 2020
In this paper, we will obtain the existence of viscosity solutions to the exterior Dirichlet problem for Hessian equations with prescribed asymptotic behavior at infinity by the Perron’s method. This extends the Ju–Bao results on Monge–Ampère equations
Hongfei Li, Limei Dai
doaj   +1 more source

On the regularity problem of complex Monge–Ampere equations with conical singularities [PDF]

Annales de l'Institut Fourier, 2017
In the category of metrics with conical singularities along a smooth divisor with angle in ( 0 , 2 π )
Chen, Xiuxiong, Wang, Yuanqi
openaire   +2 more sources

Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications

Journal of Function Spaces, 2018
We shall establish the global bifurcation results from the trivial solutions axis or from infinity for the Monge-Ampère equations: det(D2u)=λm(x)-uN+m(x)f1(x,-u,-u′,λ)+f2(x,-u,-u′,λ), in B, u(x)=0, on ∂B, where D2u=(∂2u/∂xi∂xj) is the Hessian matrix of u,
Wenguo Shen
doaj   +1 more source

The Non-Archimedean Monge-Ampere Equation

, 2015
We give an introduction to our work on the solution to the non-Archimedean Monge-Ampere equation and make comparisons to the complex counterpart. These notes are partially based on talks at the 2015 Simons Symposium on Tropical and Nonarchimedean Geometry.
Boucksom, Sebastien, Favre, Charles, Jonsson, Mattias   +2 more
openaire   +2 more sources

Solvability Criterion for a System Arising from Monge–Ampère Equations with Two Parameters

Axioms
Monge–Ampère equations have important research significance in many fields such as geometry, convex geometry and mathematical physics. In this paper, under some superlinear and sublinear conditions, the existence of nontrivial solutions for a system ...
Liangyu Wang, Hongyu Li
doaj   +1 more source

Approximate Ricci‐Flat Metrics for Calabi–Yau Manifolds

Fortschritte der Physik, Volume 74, Issue 7, July 2026.
ABSTRACT We outline a method to determine analytic Kähler potentials with associated approximately Ricci‐flat Kähler metrics on Calabi–Yau manifolds. Key ingredients are numerically calculating Ricci‐flat Kähler potentials via machine learning techniques and fitting the numerical results to Donaldson's ansatz.
Seung‐Joo Lee, Andre Lukas
wiley   +1 more source

Wall–chamber decompositions for generalised Monge–Ampère equations

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract Generalised Monge–Ampère (gMA) equations form a large class of PDE including Donaldson's J‐equation, inverse Hessian equations, some supercritical deformed Hermitian–Yang–Mills (dHYM) equations and some Z‐critical equations. Solvability of these equations is characterised by numerical criteria involving intersection numbers over all ...
Sohaib Khalid, Zakarias Sjöström Dyrefelt   +1 more
wiley   +1 more source