Global invertibility of Sobolev maps

DOI10.1515/acv-2018-0053zbMath1475.74011OpenAlexW2961759408MaRDI QIDQ831231

Marcos Oliva, Carlos Mora-Corral, Duvan Henao

Publication date: 11 May 2021

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/acv-2018-0053

zbMATH Keywords

hyperelasticitycompactness argumentglobal invertibilityminimizer existenceSobolev function traceSobolev map

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) PDEs in connection with mechanics of deformable solids (35Q74) Qualitative behavior of solutions of equilibrium problems in solid mechanics (74G55) Existence of solutions of equilibrium problems in solid mechanics (74G22)

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Cites Work

• Regularity of inverses of Sobolev deformations with finite surface energy
• Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity
• Fracture surfaces and the regularity of inverses for BV deformations
• Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity
• Cavitation, invertibility, and convergence of regularized minimizers in nonlinear elasticity
• Injectivity and self-contact in nonlinear elasticity
• Regularity properties of deformations with finite energy
• Null Lagrangians, weak continuity, and variational problems of arbitrary order
• Convexity conditions and existence theorems in nonlinear elasticity
• Relaxation of multiple integrals below the growth exponent
• An existence theory for nonlinear elasticity that allows for cavitation
• On a new class of elastic deformations not allowing for cavitation
• \(\Gamma\)-convergence approximation of fracture and cavitation in nonlinear elasticity
• A numerical study of void coalescence and fracture in nonlinear elasticity
• Lusin's condition and the distributional determinant for deformations with finite energy
• Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
• Almost-everywhere injectivity in nonlinear elasticity
• Global invertibility of Sobolev functions and the interpenetration of matter
• Local Invertibility of Sobolev Functions
• Invertibility and a Topological Property of Sobolev Maps
• Transformations by functions in Sobolev spaces and lower semicontinuity for parametric variational problems
• YOUNG MEASURES, CARTESIAN MAPS, AND POLYCONVEXITY
• The Convergence of Regularized Minimizers for Cavitation Problems in Nonlinear Elasticity
• Direct methods in the calculus of variations
• On the existence of minimizers with prescribed singular points in nonlinear elasticity
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