Free Access
Volume 27, 2021
Article Number 26
Number of page(s) 39
Published online 26 March 2021
  1. 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]
  2. J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63 (1977) 337–403. [Google Scholar]
  3. J.M. Ball, The calculus of variations and material science, Current and future challenges in the applications of mathematics, 384 (Providence, RI, 1997). Quart. Appl. Math. 56 (1998) 719–740. [CrossRef] [Google Scholar]
  4. J.M. Ball, Singularities and computation of minimizers for variational problems, Foundations of computational mathematics (Oxford, 1999). London Math. Soc. Lecture Note Ser. 284, Cambridge Univ. Press, Cambridge (2001) 1–20. [Google Scholar]
  5. J.M. Ball, Progress and puzzles in Nonlinear Elasticity, Proceedings of course on Poly-, Quasi- and Rank-One Convexity in Applied Mechanics. CISM Courses and Lectures. Springer (2010). [Google Scholar]
  6. J. Ball, J.C. Currie and P.J. Olver, Null Lagrangians, weak continuity, and variational problems of arbitrary order. J. Funct. Anal. 41 (1981) 135–174. [Google Scholar]
  7. J.M. Ball and C. Mora-Corral, A variational model allowing both smooth and sharp phase boundaries in solids. Commun. Pure Appl. Anal. 8 (2009) 55–81. [Google Scholar]
  8. D. Campbell, Diffeomorphic approximation of Planar Sobolev Homeomorphisms in Orlicz-Sobolev spaces. J. Funct. Anal. 273 (2017) 125–205. [Google Scholar]
  9. D. Campbell, L. D’Onofrio and S. Hencl, A sense preserving Sobolev homeomorphism with negative Jacobian almost every where. Preprint arXiv:2003.03214 (2020). [Google Scholar]
  10. D. Campbell, S. Hencl and V. Tengvall, Approximation of W1,p Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian. Adv. Math. 331 (2018) 748–829. [Google Scholar]
  11. D. Campbell, L. Greco, R Schiattarella and F. Soudský, Diffeomorphic approximation of Planar Sobolev Homeomorphisms in rearrangement invariant spaces. Preprint arXiv:2005.04998 (2020). [Google Scholar]
  12. P.G. Ciarlet, Mathematical Elasticity. Vol. I. Three-dimensional elasticity. Studies in Mathematics and its A, 20. North-Holland Publishing Co., Amsterdam (1987). [Google Scholar]
  13. S. Daneri and A. Pratelli, Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms. Ann. Inst. Henri Poincare Anal. Non Lineaire 31 (2014) 567–589. [Google Scholar]
  14. G. De Philippis and A. Pratelli, The closure of planar diffeomorphisms in Sobolev spaces. Ann. Inst. Henri Poincare Anal. NonLineaire 37 (2020) 181–224. [Google Scholar]
  15. L.C. Evans, Quasiconvexity and partial regularity in the calculus of variations. Ann. Math. 95 (1986) 227–252. [Google Scholar]
  16. T.J. Healey and S. Krömer, Injective weak solutions in second-gradient nonlinear elasticity. ESAIM: COCV 15 (2009) 863–871. [EDP Sciences] [Google Scholar]
  17. S. Hencl and A. Pratelli, Diffeomorphic approximation of W1;1 planar Sobolev homeomorphisms. J. Eur. Math Soc. 20 (2018) 597–656. [Google Scholar]
  18. S. Hencl and B. Vejnar, Sobolev homeomorphisms that cannot be approximated by diffeomorphisms in W1;1. Arch. Rational Mech. Anal. 219 (2016) 183–202. [Google Scholar]
  19. T. Iwaniec, L.V. Kovalev and J. Onninen, Diffeomorphic approximation of Sobolev homeomorphisms. Arch. Rational Mech. Anal. 201 (2011) 1047–1067. [Google Scholar]
  20. T. Iwaniec and J. Onninen, Monotone Sobolev mappings of planar domains and surfaces. Arch. Rational Mech. Anal. 219 (2016) 159–181. [Google Scholar]
  21. T. Iwaniec and J. Onninen, Triangulation of diffeomorphisms. Math. Ann. 368 (2017) 1133–1169. [Google Scholar]
  22. S. Krömer, Global Invertibility for Orientation-Preserving Sobolev Maps via Invertibility on or Near the Boundary. Arch. Rational Mech. Anal. 238 (2020) 1113–1155. [Google Scholar]
  23. S. Müller, Variational models for microstructure and phase transition, in Calculus of Variations and Geometric Evolution Problems, edited by S. Hildebrandt and M. Struwe. Springer-Verlag (1999) 85–210. [Google Scholar]
  24. C. Mora-Coral, Approximation by piecewise approximations of homeomorphisms of Sobolev homeomorphisms that are smooth outside a point. Houston J. Math. 35 (2009) 515–539. [Google Scholar]
  25. C. Mora-Coral and A. Pratelli, Approximation of piecewise affine homeomorphisms by diffeomorphisms. J. Geom. Anal. 24 (2014) 1398–1424. [Google Scholar]
  26. A. Pratelli and E. Radici, Approximation of planar BV homeomorphisms by diffeomorphisms. J. Funct. Anal. 276 (2019) 659–686. [Google Scholar]
  27. A. Pratelli, On the bi-Sobolev planar homeomorphisms and their approximation. Nonlinear Anal. TMA 154 (2017) 258–268. [Google Scholar]
  28. R.A. Toupin, Elastic materials with couple-stresses. Arch. Rational Mech. Anal. 11 (1962) 385–414. [Google Scholar]
  29. R.A. Toupin, Theories of elasticity with couple-stress. Arch. Rational Mech. Anal. 17 (1964) 85–112. [Google Scholar]

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