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Global invertibility of Sobolev maps

  • Duvan Henao ORCID logo , Carlos Mora-Corral ORCID logo EMAIL logo and Marcos Oliva

Abstract

We define a class of Sobolev W1,p(Ω,n) functions, with p>n-1, such that its trace on Ω is also Sobolev, and do not present cavitation in the interior or on the boundary. We show that if a function in this class has positive Jacobian and coincides on the boundary with an injective map, then the function is itself injective. We then prove the existence of minimizers within this class for the type of functionals that appear in nonlinear elasticity.


Communicated by Frank Duzaar


Award Identifier / Grant number: NC130017

Award Identifier / Grant number: 307179

Award Identifier / Grant number: 1150038

Award Identifier / Grant number: MTM2014-57769-C3-1-P

Award Identifier / Grant number: MTM2017-85934-C3-2-P

Award Identifier / Grant number: RYC-2010

Funding statement: C. Mora-Corral has been supported by the Spanish Ministry of Economy and Competitivity (Projects MTM2014-57769-C3-1-P, MTM2017-85934-C3-2-P and the “Ramón y Cajal” programme RYC-2010-06125) and the ERC Starting grant no. 307179. D. Henao has been supported by the FONDECYT project 1150038 of the Chilean Ministry of Education and the Millennium Nucleus Center for Analysis of PDE NC130017 of the Chilean Ministry of Economy.

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Received: 2018-09-04
Revised: 2019-05-08
Accepted: 2019-06-03
Published Online: 2019-07-12
Published in Print: 2021-04-01

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