A weak approach to finite elasticity

DOI10.1007/BF01234316zbMath0806.49007OpenAlexW2034302548MaRDI QIDQ1315031

Mariano Giaquinta, Jiří Souček, Giuseppe Modica

Publication date: 16 February 1995

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01234316

zbMATH Keywords

mixed boundary value problemsmeasurable mapsperfect elasticityweak deformationsweak diffeomorphisms

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Variational problems in a geometric measure-theoretic setting (49Q20) Existence theories for optimal control problems involving partial differential equations (49J20)

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A \(\Gamma\) -convergence result for thin curved films bonded to a fixed substrate with a noninterpenetration constraint, Connectivity properties of the range of a weak diffeomorphism, Analytic characterization of monotone Hopf-harmonics, Hidden Convexity in a Problem of Nonlinear Elasticity, Ground states in complex bodies

Cites Work

• Injectivity and self-contact in nonlinear elasticity
• Regularity properties of deformations with finite energy
• Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity
• Convexity conditions and existence theorems in nonlinear elasticity
• On a new class of elastic deformations not allowing for cavitation
• An introduction to continuum mechanics
• Almost-everywhere injectivity in nonlinear elasticity
• Global invertibility of Sobolev functions and the interpenetration of matter
• Area and the area formula
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