Convex integration for the Monge-Amp\`ere equation in two dimensions
Analysis of PDEs
2017-06-14 v2 Mathematical Physics
Differential Geometry
math.MP
Abstract
This paper concerns the questions of flexibility and rigidity of solutions to the Monge-Amp\`ere equation which arises as a natural geometrical constraint in prestrained nonlinear elasticity. In particular, we focus on anomalous i.e. "flexible" weak solutions that can be constructed through methods of convex integration \`a la Nash & Kuiper and establish the related h-principle for the Monge-Amp\`ere equation in two dimensions
Keywords
Cite
@article{arxiv.1508.01362,
title = {Convex integration for the Monge-Amp\`ere equation in two dimensions},
author = {Marta Lewicka and Mohammad Reza Pakzad},
journal= {arXiv preprint arXiv:1508.01362},
year = {2017}
}
Comments
30 pages, 1 figure