Free access
Volume 47, Number 4, July-August 2013
Page(s) 1133 - 1165
Published online 17 June 2013
  1. R.A. Adams and J.J.F. Fournier, Sobolev Spaces. Academic Press, Amsterdam (2003).
  2. G. Aronson, L.C. Evans and Y. Wu, Fast/slow diffusion and growing sandpiles. J. Differ. Eqn. 131 (1996) 304–335. [CrossRef]
  3. C. Bahriawati and C. Carstensen, Three Matlab implementations of the lowest-order Raviart–Thomas MFEM with a posteriori error control. Comput. Methods Appl. Math. 5 (2005) 333–361. [CrossRef] [MathSciNet]
  4. J.W. Barrett and L. Prigozhin, Dual formulations in critical state problems. Interfaces Free Bound. 8 (2006) 347–368.
  5. J.W. Barrett and L. Prigozhin, A mixed formulation of the Monge-Kantorovich equations. ESAIM: M2AN 41 (2007) 1041–1060. [CrossRef] [EDP Sciences]
  6. J.W. Barrett and L. Prigozhin, A quasi-variational inequality problem in superconductivity. M3AS 20 (2010) 679–706.
  7. S. Dumont and N. Igbida, On a dual formulation for the growing sandpile problem. Euro. J. Appl. Math. 20 (2008) 169–185. [CrossRef]
  8. S. Dumont and N. Igbida, On the collapsing sandpile problem. Commun. Pure Appl. Anal. 10 (2011) 625–638. [CrossRef] [MathSciNet]
  9. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. North-Holland, Amsterdam (1976).
  10. L.C. Evans, M. Feldman and R.F. Gariepy, Fast/slow diffusion and collapsing sandpiles. J. Differ. Eqs. 137 (1997) 166–209. [CrossRef]
  11. M. Farhloul, A mixed finite element method for a nonlinear Dirichlet problem. IMA J. Numer. Anal. 18 (1998) 121–132. [CrossRef] [MathSciNet]
  12. G.B. Folland, Real Analysis: Modern Techniques and their Applications, 2nd Edition. Wiley-Interscience, New York (1984).
  13. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd Edition. Springer, Berlin (1983).
  14. R. Glowinski, Numerical Methods for Nonlinear Variational Problems. Springer-Verlag, New York (1984).
  15. L. Prigozhin, A quasivariational inequality in the problem of filling a shape. U.S.S.R. Comput. Math. Phys. 26 (1986) 74–79. [CrossRef]
  16. L. Prigozhin, A variational model of bulk solids mechanics and free-surface segregation. Chem. Eng. Sci. 48 (1993) 3647–3656. [CrossRef]
  17. L. Prigozhin, Sandpiles and river networks: extended systems with nonlocal interactions. Phys. Rev. E 49 (1994) 1161–1167. [CrossRef] [MathSciNet]
  18. L. Prigozhin, Variational model for sandpile growth. Eur. J. Appl. Math. 7 (1996) 225–235.
  19. J.F. Rodrigues and L. Santos, Quasivariational solutions for first order quasilinear equations with gradient constraint. Arch. Ration. Mech. Anal. 205 (2012) 493–514. [CrossRef]
  20. J. Simon, Compact sets in the space Lp(0,T;B). Annal. Math. Pura. Appl. 146 (1987) 65–96. [CrossRef] [MathSciNet]
  21. J. Simon, On the existence of the pressure for solutions of the variational Navier-Stokes equations. J. Math. Fluid Mech. 1 (1999) 225–234. [CrossRef] [MathSciNet]
  22. R. Temam, Mathematical Methods in Plasticity. Gauthier-Villars, Paris (1985).

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