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2017 Convex integration for the Monge–Ampère equation in two dimensions
Marta Lewicka, Mohammad Reza Pakzad
Anal. PDE 10(3): 695-727 (2017). DOI: 10.2140/apde.2017.10.695

Abstract

This paper concerns the questions of flexibility and rigidity of solutions to the Monge–Ampère equation, which arises as a natural geometrical constraint in prestrained nonlinear elasticity. In particular, we focus on degenerate, i.e., “flexible”, weak solutions that can be constructed through methods of convex integration à la Nash and Kuiper and establish the related h-principle for the Monge–Ampère equation in two dimensions.

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Marta Lewicka. Mohammad Reza Pakzad. "Convex integration for the Monge–Ampère equation in two dimensions." Anal. PDE 10 (3) 695 - 727, 2017. https://doi.org/10.2140/apde.2017.10.695

Information

Received: 1 September 2016; Revised: 30 December 2016; Accepted: 13 February 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1370.35151
MathSciNet: MR3641884
Digital Object Identifier: 10.2140/apde.2017.10.695

Subjects:
Primary: 35M10, 76B03, 76F02

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.10 • No. 3 • 2017
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