On a new class of elastic deformations not allowing for cavitation
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Publication:1904208
DOI10.1016/S0294-1449(16)30193-7zbMath0863.49002OpenAlexW96040618MaRDI QIDQ1904208
Baisheng Yan, Stefan Müller, Tang Qi
Publication date: 1 February 1996
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=AIHPC_1994__11_2_217_0
Nonlinear elasticity (74B20) Existence theories for free problems in two or more independent variables (49J10) Implicit function theorems, Jacobians, transformations with several variables (26B10)
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Cites Work
- \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
- Injectivity and self-contact in nonlinear elasticity
- Regularity properties of deformations with finite energy
- On the integrability of the Jacobian under minimal hypotheses
- Convexity conditions and existence theorems in nonlinear elasticity
- Integrability for the Jacobian of orientation preserving mappings
- On the singular support of the distributional determinant
- On the stability of conformal mappings in multidimensional spaces
- Differential forms. With applications to the physical sciences
- Biting theorems for Jacobians and their applications
- A surprising higher integrability property of mappings with positive determinant
- Higher integrability of determinants and weak convergence in L1.
- Analytical foundations of the theory of quasiconformal mappings in R^n
- Discontinuous equilibrium solutions and cavitation in nonlinear elasticity
- Almost-everywhere injectivity in nonlinear elasticity
- Global invertibility of Sobolev functions and the interpenetration of matter
- Lusin's condition (N) and mappings of the class W1, n.
- Transformations by functions in Sobolev spaces and lower semicontinuity for parametric variational problems
- Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids
- Parametric surfaces
- Direct methods in the calculus of variations
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