EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 19 / No 2 (April-June 2013) ESAIM: COCV, 19 2 (2013) 385-403 References
Free Access
Issue
ESAIM: COCV
Volume 19, Number 2, April-June 2013
Page(s) 385 - 403
DOI https://doi.org/10.1051/cocv/2012014
Published online 10 January 2013
  1. C.J.S. Alves, On the choice of source points in the method of fundamental solutions. Eng. Anal. Bound. Elem. 33 (2009) 1348–1361. [CrossRef] [Google Scholar]
  2. C.J.S. Alves and P.R.S. Antunes, The method of fundamental solutions applied to the calculation of eigenfrequencies and eigenmodes of 2D simply connected shapes. Comput. Mater. Cont. 2 (2005) 251–266. [Google Scholar]
  3. C.J.S. Alves and P.R.S. Antunes, The method of fundamental solutions applied to the calculation of eigensolutions for 2D plates. Int. J. Numer. Methods Eng. 77 (2008) 177–194. [CrossRef] [Google Scholar]
  4. P. Antunes and P. Freitas, A numerical study of the spectral gap. J. Phys. A Math. Theor. 5 (2008) 055201. [CrossRef] [MathSciNet] [Google Scholar]
  5. P.R.S. Antunes and A. Henrot, On the range of the first two Dirichlet and Neumann eigenvalues of the Laplacian. Proc. R. Soc. London Ser. A Math. Phys. Eng. Sci. 467 (2011) 1577–1603. [Google Scholar]
  6. R.F. Bass, J. Horák and P.J. McKenna, On the lift-off constant for elastically supported plates. Proc. Amer. Math. Soc. 132 (2004) 2951–2958. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Berchio, F. Gazzola and E. Mitidieri, Positivity preserving property for a class of biharmonic elliptic problems. J. Differ. Equ. 320 (2006) 1–23. [CrossRef] [Google Scholar]
  8. D. Bucur and F. Gazzola, The first biharmonic Steklov eigenvalue : positivity preserving and shape optimization. Milan J. Math. 79 (2011) 247–258. [CrossRef] [MathSciNet] [Google Scholar]
  9. D. Bucur, A. Ferrero and F. Gazzola, On the first eigenvalue of a fourth order Steklov problem. Calc. Var. 35 (2009) 103–131. [CrossRef] [MathSciNet] [Google Scholar]
  10. G. Buttazzo, V. Ferone and B. Kawohl, Minimum problems over sets of concave functions and related questions. Math. Nachr. 173 (1995) 71–89. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Ferrero, F. Gazzola and T. Weth, On a fourth order Steklov eigenvalue problem. Analysis 25 (2005) 315–332. [CrossRef] [Google Scholar]
  12. G. Fichera, Su un principio di dualità per talune formole di maggiorazione relative alle equazioni differenziali. Atti. Accut. Naz. Lincei 19 (1955) 411–418. [Google Scholar]
  13. K. Friedrichs, Die randwert und eigenwertprobleme aus der theorie der elastischen platten. Math. Ann. 98 (1927) 205–247. [CrossRef] [Google Scholar]
  14. F. Gazzola and G. Sweers, On positivity for the biharmonic operator under Steklov boundary conditions. Arch. Ration. Mech. Anal. 188 (2008) 399–427. [CrossRef] [MathSciNet] [Google Scholar]
  15. F. Gazzola, H.C. Grunau and G. Sweers, Polyharmonic boundary value problems. Lect. Notes Math. 1991 (2010). [CrossRef] [Google Scholar]
  16. B. Kawohl and G. Sweers, On “anti”-eigenvalues for elliptic systems and a question of McKenna and Walter. Indiana Univ. Math. J. 51 (2002) 1023–1040. [CrossRef] [MathSciNet] [Google Scholar]
  17. G.R. Kirchhoff, Über das gleichgewicht und die bewegung einer elastischen scheibe. J. Reine Angew. Math. 40 (1850) 51–88. [Google Scholar]
  18. J.R. Kuttler, Remarks on a Stekloff eigenvalue problem. SIAM J. Numer. Anal. 9 (1972) 1–5. [CrossRef] [MathSciNet] [Google Scholar]
  19. R.S. Lakes, Foam structures with a negative Poisson’s ratio. Science 235 (1987) 1038–1040. [CrossRef] [PubMed] [Google Scholar]
  20. J.L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications. Travaux et Recherches Mathématiques 3 (1970). [Google Scholar]
  21. G. Liu, The Weyl-type asymptotic formula for biharmonic Steklov eigenvalues on Riemannian manifolds. Adv. Math. 228 (2011) 2162–2217. [CrossRef] [MathSciNet] [Google Scholar]
  22. A.E.H. Love, A treatise on the mathematical theory of elasticity, 4th edition. Cambridge Univ. Press (1927). [Google Scholar]
  23. P.J. McKenna and W. Walter, Nonlinear oscillations in a suspension bridge. Arch. Ration. Mech. Anal. 98 (1987) 167–177. [CrossRef] [Google Scholar]
  24. E. Parini and A. Stylianou, On the positivity preserving property of hinged plates. SIAM J. Math. Anal. 41 (2009) 2031–2037. [CrossRef] [MathSciNet] [Google Scholar]
  25. L.E. Payne, Bounds for the maximum stress in the Saint Venant torsion problem. Special issue presented to Professor Bibhutibhusan Sen on the occasion of his seventieth birthday, Part I. Indian J. Mech. Math. (1968/1969) 51–59. [Google Scholar]
  26. L.E. Payne, Some isoperimetric inequalities for harmonic functions. SIAM J. Math. Anal. 1 (1970) 354–359. [CrossRef] [MathSciNet] [Google Scholar]
  27. R. Schneider, Convex bodies : the Brunn-Minkowski theory. Cambridge Univ. Press (1993). [Google Scholar]
  28. J. Smith, The coupled equation approach to the numerical solution of the biharmonic equation by finite differences I. SIAM J. Numer. Anal. 5 (1968) 323–339. [CrossRef] [MathSciNet] [Google Scholar]
  29. J. Smith, The coupled equation approach to the numerical solution of the biharmonic equation by finite differences II. SIAM J. Numer. Anal. 7 (1970) 104–111. [CrossRef] [MathSciNet] [Google Scholar]
  30. W. Stekloff, Sur les problèmes fondamentaux de la physique mathématique. Ann. Sci. Éc. Norm. Sup. 19 (1902) 191–259; 455–490. [Google Scholar]
  31. Wikipedia, the Free Encyclopedia, available on http://en.wikipedia.org/wiki/Reuleaux♯triangle♯Reuleaux−polygons [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.