Global invertibility of Sobolev maps-Reference-Cited by-同舟云学术

Global invertibility of Sobolev maps

Published:2019-07-12 Issue:2 Volume:14 Page:207-230
ISSN:1864-8266
Container-title:Advances in Calculus of Variations
language:en
Short-container-title:

Author:

Henao Duvan¹^ORCID,Mora-Corral Carlos²^ORCID,Oliva Marcos³

Affiliation:

1. Facultad de Matemáticas , Pontificia Universidad Catolica de Chile , Santiago , Chile

2. Department of Mathematics , Universidad Autonoma de Madrid , Madrid , Spain

3. PiperLab , Madrid , Spain

Abstract

Abstract We define a class of Sobolev W 1 , p ⁢ ( Ω , ℝ n )

{W^{1,p}(\Omega,\mathbb{R}^{n})}

functions, with p > n - 1

{p>n-1}

, such that its trace on ∂ ⁡ Ω

{\partial\Omega}

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.

Funder

Ministerio de Economía, Fomento y Turismo

FP7 Ideas: European Research Council

Fondo Nacional de Desarrollo Científico y Tecnológico

Ministerio de Economía y Competitividad

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/acv-2018-0053/pdf

Reference43 articles.

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