EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 31 (2025) ESAIM: COCV, 31 (2025) 39 References
Open Access
Issue
ESAIM: COCV
Volume 31, 2025
Article Number 39
Number of page(s) 24
DOI https://doi.org/10.1051/cocv/2025028
Published online 16 April 2025
  1. J.M. Ball, Global invertibility of Sobolev functions and the interpenetration of matter. Proc. Roy. Soc. Edinburgh Sect. A 88 (1981) 315–328. [Google Scholar]
  2. P.G. Ciarlet and J. NeCas, Injectivity and self-contact in nonlinear elasticity. Arch. Rational Mech. Anal. 97 (1987) 171–188. [Google Scholar]
  3. D. Henao and C. Mora-Corral, Invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity. Arch. Rational Mech. Anal 197 (2010) 619–655. [CrossRef] [MathSciNet] [Google Scholar]
  4. D. Henao and C. Mora-Corral, Lusin’s condition and the distributional determinant for deformations with finite energy. Adv. Calc. Var. 5 (2012) 355–409. [Google Scholar]
  5. S. Müller, T. Qi and B.S. Yan, On a new class of elastic deformations not allowing for cavitation. Ann. l’I.H.P. Analyse non linéaire 11 (1994) 217–243. [Google Scholar]
  6. S. Müller and S.J. Spector, An existence theory for nonlinear elasticity that allows for cavitation. Arch. Ration. Mech. Anal. 131 (1995) 1–66. [Google Scholar]
  7. V. Šverák, Regularity properties of deformations with finite energy. Arch. Ration. Mech. Anal. 100 (1998) 105–127. [Google Scholar]
  8. D. Henao, C. Mora-Corral and M. Oliva, Global invertibility of Sobolev maps. Adv. Calc. Var. 14 (2021) 207–230. [Google Scholar]
  9. S. Krüomer, Global invertibility for orientation-preserving Sobolev maps via invertibility on or near the boundary. Arch. Ration. Mech. Anal. 238 (2020) 1113–1155. [Google Scholar]
  10. S. Müller, Det = det. A remark on the distributional determinant. C. R. Acad. Sci. Paris Ser. I Math. 311 (1990) 13–17. [Google Scholar]
  11. S. Muüller, Weak continuity of determinants and nonlinear elasticity. C. R. Acad. Sci. Paris Seer. I Math. 307 (1988) 501–506. [Google Scholar]
  12. M. Barchiesi, D. Henao and C. Mora-Corral, Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity. Arch. Ration. Mech. Anal. 224 (2017) 743–816. [Google Scholar]
  13. D. Henao and C. Mora-Corral, Fracture surfaces and the regularity of inverses for BV deformations. Arch. Ration. Mech. Anal. 201 (2011) 575–629. [Google Scholar]
  14. P.G. Ciarlet, Mathematical Elasticity. Vol. I. Vol. 20 of Studies in Mathematics and its Applications. North-Holland Publishing Co., Amsterdam (1988). [Google Scholar]
  15. P. Podio-Guidugli and G. Vergara Caffarelli, Surface interaction potentials in elasticity. Arch. Rational Mech. Anal. 109 (1990) 343–383. [Google Scholar]
  16. N.C. Owen and P. Sternberg, Gradient flow and front propagation with boundary contact energy. Proc. Roy. Soc. London Ser. A 437 (1992) 715–728. [CrossRef] [MathSciNet] [Google Scholar]
  17. B. Dacorogna, I. Fonseca, J. Maly and K. Trivisa, Manifold constrained variational problems. Calc. Var. Part. Differ. Equ. 9 (1999) 185–206. [Google Scholar]
  18. M. Silhavy, Equilibrium of phases with interfacial energy: a variational approach. J. Elast. 105 (2011) 271–303. [Google Scholar]
  19. H. Federer, Geometric Measure Theory. Springer-New York (1969). [Google Scholar]
  20. K. Deimling, Nonlinear Functional Analysis. Springer-Verlag (1985). [CrossRef] [Google Scholar]
  21. A. Czarnecki, M. Kulczycki and W. Lubawski, On the connectedness of boundary and complement for domains. Ann. Pol. Math. 103 (2012) 189–191. [Google Scholar]
  22. M. Bresciani, M. Friedrich and C. Mora-Corral, Variational models with Eulerian-Lagrangian formulation allowing for material failure. Avaliable at: https://arxiv.org/abs/2402.12870v1 (2024). [Google Scholar]
  23. P. Bernard and U. Bessi, Young measures, Cartesian maps, and polyconvexity. J. Korean Math. Soc. 47 (2010) 331–350. [Google Scholar]
  24. B. Dacorogna, Direct Methods in the Calculus of Variations. Springer-New York (2008). [Google Scholar]
  25. R. Alicandro and C. Leone, 3D-2D asymptotic analysis for micromagnetic thin films. ESAIM Control Optim. Calc. Var. 6 (2001) 489–498. [Google Scholar]
  26. C. Mora-Corral and M. Oliva, Relaxation of nonlinear elastic energies involving the deformed configuration and applications to nematic elastomers. ESAIM Control Optim. Calc. Var. 25 (2019). [Google Scholar]
  27. J.A. Thorpe, Elementary Topics in Differential Geometry. Springer New York (1979). [CrossRef] [Google Scholar]
  28. J.P. Aubin and H. Frankowska, Set-Valued Analysis. Birkhüauser Boston, MA (2008). [Google Scholar]
  29. I. Fonseca and G. Leoni, Modern Methods in the Calculus of Variations: Lp Spaces. Springer Monogr. Math. Springer-New York (2007). [Google Scholar]
  30. J.M. Ball, J.C. Currie and P.J. Olver. Null Lagrangians, weak continuity, and variational problems of arbitrary order. J. Funct. Anal. 41 (1991) 135–174. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.