Open Access
Volume 30, 2024
Article Number 37
Number of page(s) 32
Published online 23 April 2024
  1. J.M. Ball, Convexity conditions and existence theorems in nonlinear Elasticity. Arch. Ration. Mech. Anal. 63 (1977) 337–403. [Google Scholar]
  2. P.G. Ciarlet and J. Nečas, Injectivity and self-contact in nonlinear Elasticity. Arch. Ration. Mech. Anal. 97 (1987) 171–188. [Google Scholar]
  3. A. Doležalová, S. Hencl and J. Malý, Weak limit of homeomorphisms in W1,n−1 and (INV) condition. Arch. Ration. Mech. Anal. 247 (2023). [Google Scholar]
  4. S. Müller and S. Spector, An existence theory for nonlinear elasticity that allows for cavitation. Arch. Ration. Mech. Anal. 131 (1995) 1–66. [Google Scholar]
  5. 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]
  6. 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]
  7. 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]
  8. D. Henao, C. Mora-Corral and M. Oliva, Global invertibility of Sobolev maps. Adv. Calc. Var. 14 (2019) 207–230. [Google Scholar]
  9. S. Müller, S. Spector and Q. Tang, Invertibility and a topological property of Sobolev maps. SIAM J. Math. Anal. 27 (1996) 959–976. [Google Scholar]
  10. D. Swanson and W. P. Ziemer, A topological aspect of Sobolev mappings. Calc. Var. Partial Differ. Equ. 14 (2002) 69–84. [Google Scholar]
  11. D. Swanson and W.P. Ziemer, The image of a weakly differentiable mapping. SIAM J. Math. Anal. 35 (2004) 1099–1109. [Google Scholar]
  12. Q. Tang, Almost-everywhere injectivity in nonlinear elasticity. Proc. Roy. Soc. Edinburgh Sect. A 109 (1998) 79–95. [Google Scholar]
  13. G. Scilla and B. Stroffolini, Invertibility of Orlicz–Sobolev maps, in Research in Mathematics of Materials Science. Assoc. Women Math. Ser., Vol. 31. (2022) 297–317. [Google Scholar]
  14. S. Conti and C. De Lellis, Some remarks on the theory of elasticity for compressible Neohookean materials. Ann. Sc. Norm. Super. Pisa Cl. Sci. 2 (2003) 521–549. [Google Scholar]
  15. M. Barchiesi, D. Henao, C. Mora-Corral and R. Rodiac, Harmonic dipoles and the relaxation of the neo-hookean energy in 3d elasticity. Arch. Ration. Mech. Anal. 247 (2023). [Google Scholar]
  16. M. Barchiesi, D. Henao, C. Mora-Corral and R. Rodiac, On the lack of compactness problem in the axisymmetric neo-Hookean model. 2021. [Google Scholar]
  17. O. Bouchala, S. Hencl and A. Molchanova, Injectivity almost everywhere for weak limits of Sobolev homeomorphisms. J. Funct. Anal. 279 (2020) 108658. [Google Scholar]
  18. T. Iwaniec and J. Onninen, Monotone Sobolev mappings of planar domains and Surfaces. Arch. Ration. Mech. Anal. 219 (2016) 159–181. [Google Scholar]
  19. T. Iwaniec and J. Onninen, Limits of Sobolev homeomorphisms. J. Eur. Math. Soc. 19 (2017) 473–505. [Google Scholar]
  20. G. De Philippis and A. Pratelli, The closure of planar diffeomorphisms in Sobolev spaces. Ann. Inst. H. Poincaré C Anal. Non Linéaire 37 (2020) 181–224. [Google Scholar]
  21. J. Spector, Q. Tang and B.S. Yan, On a new class of elastic deformations not allowing for cavitation. Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994) 217–243. [Google Scholar]
  22. M. Csörnyei, S. Hencl and J. Malý, Homeomorphisms in the Sobolev space W1,n−1. J. Reine Angew. Math. 644 (2010) 221–235. [Google Scholar]
  23. L. D’Onofrio and R. Schiattarella, On the total variations for the inverse of a BV-homeomorphism. Adv. Calc. Var. 6 (2013) 321–338. [Google Scholar]
  24. J.M. Ball and F. Murat, W1,p-quasiconvexity and variational problems for multiple integrals. J. Funct. Anal. 58 (1984) 225–253. [Google Scholar]
  25. J. Malý, Weak lower semicontinuity of polyconvex integrals. Proc. Roy. Soc. Edinburgh Sect. A 123 (1993) 681–691. [Google Scholar]
  26. G. Dal Maso and C. Sbordone, Weak lower semicontinuity of polyconvex integrals: a borderline case. Math. Z. 218 (1995) 603–609. [Google Scholar]
  27. P. Celada and G. Dal Maso, Further remarks on the lower semicontinuity of polyconvex integrals. Ann. Inst. H. Poincaré C Anal. Non Linéaire 11 (1994) 661–691. [Google Scholar]
  28. S. Hencl and P. Koskela, Lectures on Mappings of Finite Distortion. Lecture Notes in Mathematics, Vol. 2096, Springer International Publishing (2014). [Google Scholar]
  29. H. Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, 2nd edn. Springer-Verlag, New York (1969). [Google Scholar]
  30. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York (2000). [Google Scholar]
  31. M. Giaquinta, G. Modica and J. Souček, Cartesian currents in the calculus of variations. I. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, Vol. 37. Springer-Verlag, Berlin (1998). [Google Scholar]
  32. G. Leoni, A First Course in Sobolev Spaces, Vol. 181 of Graduate Studies in Mathematics, 2nd edn. American Mathematical Society, Providence, RI (2017). [Google Scholar]
  33. B. Dacorogna, Direct Methods in the Calculus of Variations. Vol. 78 of Applied Mathematical Sciences, 2nd edn. Springer, New York (2008). [Google Scholar]
  34. N. Fusco, G. Moscariello and C. Sbordone, The limit of W1,1 homeomorphisms with finite distortion. Calc. Var. Partial Differ. Equ. bf 33 (2008) 377–390. [Google Scholar]
  35. P. Harjulehto and P. Hästö, Orlicz Spaces and Generalized Orlicz Spaces, Vol. 2236 of Lecture Notes in Mathematics. Springer, Cham (2019). [Google Scholar]
  36. S. Hencl and J. Malý, Jacobians of Sobolev homeomorphisms. Calc. Var. Partial Differ. Equ. 38 (2010) 233–242. [Google Scholar]
  37. H. Brezis and L. Nirenberg, Degree theory and BMO. I. Compact manifolds without boundaries. Selecta Math. (N.S.) 1 (1995) 197–263. [Google Scholar]
  38. L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics. CRC Press, Boca Raton, FL (1992) viii+268. [Google Scholar]
  39. J. Malý and O. Martio, Lusin’s condition (N) and mappings of the class W1,n. J. Reine Angew. Math. 458 (1995) 19–36. [MathSciNet] [Google Scholar]
  40. F. Rindler, Calculus of variations, Universitext. Springer, Cham (2018) 444. [Google Scholar]
  41. P.G. Ciarlet, Mathematical Elasticity, Vol. I: Three-Dimensional Elasticity, Series “Studies in Mathematics and its Applications”. (1988). [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.