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Convex integration
for the Monge–Ampère equation in two dimensions
Marta Lewicka and Mohammad Reza Pakzad |
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Vol. 10 (2017), No. 3, 695–727
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Abstract |
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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 -principle for the Monge–Ampère equation in two dimensions. An errata was submitted on 23 Aug 2023 and posted online on 30 Jan 2024. (Theorem 1.4 is unproved.) |
Keywords
Monge–Ampére equation, convex integration, $h$-principle,
rigidity and flexibility, developable surfaces
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Mathematical Subject Classification 2010
Primary: 35M10, 76B03, 76F02
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Supplementary material |
Milestones
Received: 1 September 2016
Revised: 30 December 2016
Accepted: 13 February 2017
Published: 17 April 2017
Errata: 30 January 2024 |
Authors |
| Marta Lewicka | |
| Department of Mathematics University of Pittsburgh 139 University Place Pittsburgh, PA 15260 United States |
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| Mohammad Reza Pakzad | |
| Department of Mathematics University of Pittsburgh 139 University Place Pittsburgh, PA 15260 United States |
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| © 2017 MSP (Mathematical Sciences Publishers). |
