Optimization approach for the Monge-Ampère equation

DOI10.1016/S0252-9602(18)30814-2zbMath1438.35137arXiv1701.05388OpenAlexW2963670271MaRDI QIDQ2313143

Fethi Ben Belgacem

Publication date: 18 July 2019

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.05388

zbMATH Keywords

finite element Galerkin methodelliptic Monge-Ampère equationgradient conjugate method

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Nonlinear elliptic equations (35J60) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Cites Work

• Vanishing moment method and moment solutions for fully nonlinear second order partial differential equations
• Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian
• A nonconforming Morley finite element method for the fully nonlinear Monge-Ampère equation
• The Monge-Ampère equation: various forms and numerical solution
• The Dirichlet problem for the degenerate Monge-Ampère equation
• On the numerical solution of the equation \(\frac{\partial ^ 2z\partial ^ 2z}{\partial x^ 2\partial y^ 2}-(\frac{\partial ^ 2z}{\partial x\partial y})^ 2=f\) and its discretizations. I
• Numerical solution of the two-dimensional elliptic Monge--Ampère equation with Dirichlet boundary conditions: An augmented Lagrangian approach
• A Liouville theorem for solutions of the Monge--Ampère equation with periodic data.
• Topics in regularity and qualitative properties of solutions of nonlinear elliptic equations
• Numerical solution of the two-dimensional elliptic Monge--Ampère equation with Dirichlet boundary conditions: a least-squares approach
• Numerical methods for fully nonlinear elliptic equations of the Monge-Ampère type
• Minimization of functions having Lipschitz continuous first partial derivatives
• Two Numerical Methods for the elliptic Monge-Ampère equation
• On Finite Element Methods for Fully Nonlinear Elliptic Equations of Second Order
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• Determination of reflector surfaces from near-field scattering data
• The Monge–Kantorovitch mass transfer and its computational fluid mechanics formulation
• Deformations of density functions in molecular quantum chemistry
• Convergence Conditions for Ascent Methods
• On Steepest Descent
• The conjugate gradient method in extremal problems
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