Open Access
Volume 28, 2022
Article Number 29
Number of page(s) 29
Published online 25 May 2022
  1. S. Adly and L. Bourdin, Sensitivity analysis of variational inequalities via twice epi-differentiability and proto-differentiability of the proximity operator. SIAM J. Optim. 28 (2018) 1699–1725. [CrossRef] [MathSciNet] [Google Scholar]
  2. J.M. Aitchison and M.W. Poole, A numerical algorithm for the solution of Signorini problems. J. Comput. Appl. Math. 94 (1998) 55–67. [CrossRef] [MathSciNet] [Google Scholar]
  3. J. Andersson, Optimal regularity for the Signorini problem and its free boundary. Invent. Math. 204 (2016) 1–82. [CrossRef] [MathSciNet] [Google Scholar]
  4. S.S. Antman, The influence of elasticity on analysis: modern developments. Bull. Am. Math. Soc. (N.S.) 9 (1983) 267–291. [CrossRef] [Google Scholar]
  5. H. Attouch, Variational convergence for functions and operators, Applicable Mathematics Series, Pitman (Advanced Publishing Program), Boston, MA (1984). [Google Scholar]
  6. F. Ben Belgacem and Y. Renard, Hybrid finite element methods for the Signorini problem. Math. Comp. 72 (2003) 1117–1145. [CrossRef] [MathSciNet] [Google Scholar]
  7. H. Brezis, Functional analysis, Sobolev spaces and partial differential equations. Universitext, Springer, New York (2011). [Google Scholar]
  8. F. Chouly and P. Hild, A Nitsche-based method for unilateral contact problems: numerical analysis. SIAM J. Numer. Anal. 51 (2013) 1295–1307. [CrossRef] [MathSciNet] [Google Scholar]
  9. C.N. Do, Generalized second-order derivatives of convex functions in reflexive Banach spaces. Trans. Am. Math. Soc. 334 (1992) 281–301. [CrossRef] [Google Scholar]
  10. G. Duvaut and J.-L. Lions, Inequalities in mechanics and physics. Translated from the French by C.W. John, Grundlehren der Mathematischen Wissenschaften, 219. Springer-Verlag, Berlin-New York (1976). [Google Scholar]
  11. L.C. Evans, Partial differential equations., Vol. 19 of Graduate Studies in Mathematics. 2nd edn., American Mathematical Society, Providence, RI (2010). [CrossRef] [Google Scholar]
  12. G. Fichera, Problemi elastostatici con vincoli unilaterali: Il problema di Signorini con ambigue condizioni al contorno. Atti Accad. Naz. Lincei Mem. Cl. Sci. Fis. Mat. Natur. Sez. I 7 (1963/1964) 91–140. [Google Scholar]
  13. V. Girault and P.-A. Raviart, Finite element methods for Navier-Stokes equations., Vol. 5 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (1986). [CrossRef] [Google Scholar]
  14. R. Glowinski, Numerical methods for nonlinear variational problems. Springer Series in Computational Physics. SpringerVerlag, New York (1984). [Google Scholar]
  15. R. Glowinski, J.-L. Lions and R. Trémolières, Numerical analysis of variational inequalities., Vol. 8 of Studies in Mathematics and its Applications. Translated from the French. North-Holland Publishing Co., Amsterdam-New York (1981). [Google Scholar]
  16. J. Gwinner and E.P. Stephan, Advanced boundary element methods., Vol. 52 of Springer Series in Computational Mathematics. Springer, Cham (2018). [CrossRef] [Google Scholar]
  17. J. Haslinger, I. Hlavécek and J. Necas, Numerical methods for unilateral problems in solid mechanics, in Handbook of numerical analysis, North-Holland, Amsterdam (1996) 313–485. [Google Scholar]
  18. F. Hecht, New development in freefem++. J. Numer. Math. 20 (2012) 251–265. [CrossRef] [MathSciNet] [Google Scholar]
  19. P. Hild and Y. Renard, A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics. Numer. Math. 115 (2010) 101–129. [CrossRef] [MathSciNet] [Google Scholar]
  20. N. Kikuchi and J.T. Oden, Contact problems in elasticity: a study of variational inequalities and finite element methods. Vol. 8 of SIAM Studies in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (1988). [Google Scholar]
  21. D. Kinderlehrer, Remarks about Signorini’s problem in linear elasticity. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 8 (1981) 605–645. [MathSciNet] [Google Scholar]
  22. J.-L. Lions, Sur les problèmes unilatéraux, in Séminaire Bourbaki. Vol. 1968/69: Exposés 347–363. Lecture Notes in Math., vol. 175, Exp. No. 350, 55–77. Springer, Berlin (1971). [CrossRef] [Google Scholar]
  23. G.J. Minty, Monotone (nonlinear) operators in Hilbert space. Duke Math. J. 29 (1962) 341–346. [CrossRef] [MathSciNet] [Google Scholar]
  24. J.-J. Moreau, Fonctions convexes duales et points proximaux dans un espace hilbertien. C. R. Acad. Sci. Paris 255 (1962) 2897–2899. [MathSciNet] [Google Scholar]
  25. J.-J. Moreau, Proximité et dualité dans un espace hilbertien. Bull. Soc. Math. France 93 (1965) 273–299. [CrossRef] [Google Scholar]
  26. D. Noll, Second order differentiability of integral functionals on Sobolev spaces and L2-spaces. J. Reine Angew. Math. 436 (1993) 1–17. [MathSciNet] [Google Scholar]
  27. R.T. Rockafellar, On the maximal monotonicity of subdifferential mappings. Pacific J. Math. 33 (1970) 209–216. [CrossRef] [MathSciNet] [Google Scholar]
  28. R.T. Rockafellar, Maximal monotone relations and the second derivatives of nonsmooth functions. Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985) 167–184. [CrossRef] [MathSciNet] [Google Scholar]
  29. R.T. Rockafellar, Generalized second derivatives of convex functions and saddle functions. Trans. Am. Math. Soc. 322 (1990) 51–77. [CrossRef] [Google Scholar]
  30. R.T. Rockafellar and R.J.-B. Wets, Variational analysis. Vol. 317 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (1998). [CrossRef] [Google Scholar]
  31. R. Schumann, Regularity for Signorini’s problem in linear elasticity. Manuscr. Math. 63 (1989) 255–291. [CrossRef] [Google Scholar]
  32. M. Shillor, M. Sofonea and J. Telega, Models and analysis of quasistatic: variational methods. Springer-Verlag (2004). [Google Scholar]
  33. A. Signorini, Sopra alcune questioni di statica dei sistemi continui. Ann. Scuola Norm. Super. Pisa Cl. Sci. 2 (1933) 231–251. [MathSciNet] [Google Scholar]
  34. A. Signorini, Questioni di elasticitè non linearizzata e semilinearizzata. Rend. Mat. e Appl. 18 (1959) 95–139. [MathSciNet] [Google Scholar]
  35. M. Sofonea and A. Matei, Variational inequalities with applications. Vol. 18 of Advances in Mechanics and Mathematics. Springer, New York (2009). [Google Scholar]
  36. M. Tucsnak and G. Weiss, Observation and control for operator semigroups, Birkhäuser Advanced Texts: Basler Lehrbucher. Birkhäuser Verlag, Basel (2009). [Google Scholar]

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