Symmetry in the Numerical Resolution of the Elliptic Monge-Ampere Equation

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 December 2015) | Viewed by 8428

Special Issue Editor


E-Mail Website
Guest Editor
Department of Mathematics, Statistics, and Computer Science, University of Illinois, Chicago, Chicago, IL 60607-7045, USA

Special Issue Information

Dear Colleagues,

The Monge-Ampere equation is a fully nonlinear partial differential equation which appears in a wide range of applications, e.g., optimal transportation and reflector design. One notion of the weak solution of the equation is based on the old technique of approximation by smooth functions. For smooth solutions, the equation consists in prescribing the determinant of the Hessian matrix, a symmetric matrix field.

This Special Issue of Symmetry features articles with proven convergence proofs for smooth solutions and numerically robust to handle non smooth solutions.

Prof. Dr. Gerard Awanou
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


Keywords

  • Monge-Ampere
  • classical solutions
  • symmetric matrix fields
  • convergence
  • approximation by smooth functions

Published Papers (2 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

355 KiB  
Article
Convergence Rate of a Stable, Monotone and Consistent Scheme for the Monge-Ampère Equation
by Gerard Awanou
Symmetry 2016, 8(4), 18; https://doi.org/10.3390/sym8040018 - 24 Mar 2016
Cited by 3 | Viewed by 3804
Abstract
We prove a rate of convergence for smooth solutions of the Monge-Ampère equation of a stable, monotone and consistent discretization. We consider the Monge-Ampère equation with a small low order perturbation. With such a perturbation, we can prove uniqueness of a solution to [...] Read more.
We prove a rate of convergence for smooth solutions of the Monge-Ampère equation of a stable, monotone and consistent discretization. We consider the Monge-Ampère equation with a small low order perturbation. With such a perturbation, we can prove uniqueness of a solution to the discrete problem and stability of the discrete solution. The discretization considered is then known to converge to the viscosity solution but no rate of convergence was known. Full article
229 KiB  
Article
A Monge–Ampere Equation with an Unusual Boundary Condition
by Marc Sedjro
Symmetry 2015, 7(4), 2009-2024; https://doi.org/10.3390/sym7042009 - 5 Nov 2015
Cited by 1 | Viewed by 4272
Abstract
We consider a class of Monge–Ampere equations where the convex conjugate of the unknown function is prescribed on a boundary of its domain yet to be determined. We show the existence of a weak solution. Full article
Back to TopTop