Free Access
Volume 17, Number 1, January-March 2011
Page(s) 52 - 85
DOI https://doi.org/10.1051/cocv/2009043
Published online 30 October 2009
  1. L. Ambrosio, N. Gigli and G. Savaré, Gradient flows in metric spaces and in the space of probability measures, Lectures in Mathematics, ETH Zürich. Birkhäuser Verlag, Basel, Switzerland (2005). [Google Scholar]
  2. C. Baiocchi and G. Savaré, Singular perturbation and interpolation. Math. Models Methods Appl. Sci. 4 (1994) 557–570. [CrossRef] [MathSciNet] [Google Scholar]
  3. V. Barbu, Nonlinear semigroups and differential equations in Banach spaces. Noordhoff International Publishing, Leyden, The Netherlands (1976). [Google Scholar]
  4. J. Bergh and J. Löfström, Interpolation spaces. An introduction, Grundlehren der Mathematischen Wissenschaften 223. Springer-Verlag, Berlin, Germany (1976). [Google Scholar]
  5. M.A. Biot, Variational principles in irreversible thermodynamics with application to viscoelasticity. Phys. Rev. (2) 97 (1955) 1463–1469. [CrossRef] [MathSciNet] [Google Scholar]
  6. D. Brézis, Classes d'interpolation associées à un opérateur monotone. C. R. Acad. Sci. Paris Sér. A-B 276 (1973) A1553–A1556. [Google Scholar]
  7. H. Brezis, Monotonicity methods in Hilbert spaces and some application to nonlinear partial differential equations, in Contrib. to nonlin. functional analysis, Proc. Sympos. Univ. Wisconsin, Madison, Academic Press, New York, USA (1971) 101–156. [Google Scholar]
  8. H. Brezis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North Holland Math. Studies 5. Amsterdam, North-Holland (1973). [Google Scholar]
  9. H. Brezis, Interpolation classes for monotone operators, in Partial differential equations and related topics (Program, Tulane Univ., New Orleans, 1974), Lecture Notes in Math. 446, Springer, Berlin, Germany (1975) 65–74. [Google Scholar]
  10. H. Brezis and I. Ekeland, Un principe variationnel associé à certaines équations paraboliques. Le cas indépendant du temps. C. R. Acad. Sci. Paris Sér. A-B 282 (1976) A971–A974. [Google Scholar]
  11. H. Brezis and I. Ekeland, Un principe variationnel associé à certaines équations paraboliques. Le cas dépendant du temps. C. R. Acad. Sci. Paris Sér. A-B 282 (1976) A1197–A1198. [Google Scholar]
  12. F.H. Clarke, Optimization and nonsmooth analysis, Classics in Applied Mathematics 5. Second edition, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, USA (1990). [Google Scholar]
  13. S. Conti and M. Ortiz, Minimum principles for the trajectories of systems governed by rate problems. J. Mech. Phys. Solids 56 (2008) 1885–1904. [CrossRef] [MathSciNet] [Google Scholar]
  14. M.G. Crandall and A. Pazy, Semi-groups of nonlinear contractions and dissipative sets. J. Funct. Anal. 3 (1969) 376–418. [Google Scholar]
  15. E. De Giorgi, Conjectures concerning some evolution problems. Duke Math. J. 81 (1996) 255–268. A celebration of John F. Nash, Jr. [CrossRef] [MathSciNet] [Google Scholar]
  16. N. Ghoussoub, Selfdual partial differential systems and their variational principles, Springer Monographs in Mathematics. Springer, New York, USA (2009). [Google Scholar]
  17. M.E. Gurtin, Variational principles in the linear theory of viscoelasticity. Arch. Ration. Mech. Anal. 13 (1963) 179–191. [Google Scholar]
  18. M.E. Gurtin, Variational principles for linear elastodynamics. Arch. Ration. Mech. Anal. 16 (1964) 34–50. [Google Scholar]
  19. M.E. Gurtin, Variational principles for linear initial value problems. Quart. Appl. Math. 22 (1964) 252–256. [Google Scholar]
  20. I. Hlaváček, Variational principles for parabolic equations. Appl. Math. 14 (1969) 278–297. [Google Scholar]
  21. T. Ilmanen, Elliptic regularization and partial regularity for motion by mean curvature, Mem. Amer. Math. Soc. 108. American Mathematical Society, USA (1994). [Google Scholar]
  22. R.V. Kohn and S. Müller, Surface energy and microstructure in coherent phase transitions. Comm. Pure Appl. Math. 47 (1994) 405–435. [CrossRef] [MathSciNet] [Google Scholar]
  23. Y. Kōmura, Nonlinear semi-groups in Hilbert space. J. Math. Soc. Japan 19 (1967) 493–507. [CrossRef] [MathSciNet] [Google Scholar]
  24. J.-L. Lions and E. Magenes, Non-homogeneus boundary value problems and applications 1. Springer-Verlag, New York-Heidelberg (1972). [Google Scholar]
  25. A. Marino, C. Saccon and M. Tosques, Curves of maximal slope and parabolic variational inequalities on nonconvex constraints. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989) 281–330. [MathSciNet] [Google Scholar]
  26. A. Mielke and M. Ortiz, A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems. ESAIM: COCV 14 (2008) 494–516. [CrossRef] [EDP Sciences] [Google Scholar]
  27. A. Mielke and U. Stefanelli, A discrete variational principle for rate-independent evolution. Adv. Calc. Var. 1 (2008) 399–431. [CrossRef] [MathSciNet] [Google Scholar]
  28. B. Nayroles, Deux théorèmes de minimum pour certains systèmes dissipatifs. C. R. Acad. Sci. Paris Sér. A-B 282 (1976) A1035–A1038. [Google Scholar]
  29. B. Nayroles, Un théorème de minimum pour certains systèmes dissipatifs. Variante hilbertienne. Travaux Sém. Anal. Convexe 6 (1976) 22. [Google Scholar]
  30. R. Nochetto, G. Savaré and C. Verdi, A posteriori error estimates for variable time-step discretization of nonlinear evolution equations. Comm. Pure Appl. Math. 53 (2000) 525–589. [CrossRef] [MathSciNet] [Google Scholar]
  31. M. Ortiz, E.A. Repetto and H. Si, A continuum model of kinetic roughening and coarsening in thin films. J. Mech. Phys. Solids 47 (1999) 697–730. [CrossRef] [MathSciNet] [Google Scholar]
  32. F. Otto, The geometry of dissipative evolution equations: the porous medium equation. Comm. Partial Differential Equations 26 (2001) 101–174. [CrossRef] [MathSciNet] [Google Scholar]
  33. R. Rossi and G. Savaré, Gradient flows of non convex functionals in Hilbert spaces and applications. ESAIM: COCV 12 (2006) 564–614. [CrossRef] [EDP Sciences] [Google Scholar]
  34. R. Rossi, A. Mielke and G. Savaré, A metric approach to a class of doubly nonlinear evolution equations and applications. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) VII (2008) 97–169. [Google Scholar]
  35. R. Rossi, A. Segatti and U. Stefanelli, Attractors for gradient flows of non convex functionals and applications. Arch. Ration. Anal. Mech. 187 (2008) 91–135. [CrossRef] [Google Scholar]
  36. G. Savaré, Weak solutions and maximal regularity for abstract evolution inequalities. Adv. Math. Sci. Appl. 6 (1996) 377–418. [MathSciNet] [Google Scholar]
  37. J. Simon, Compact sets in the space Lp(0, T; B). Ann. Mat. Pura Appl. (4) 146 (1987) 65–96. [Google Scholar]
  38. U. Stefanelli, The Brezis-Ekeland principle for doubly nonlinear equations. SIAM J. Contr. Opt. 47 (2008) 1615–1642. [Google Scholar]
  39. U. Stefanelli, A variational principle for hardening elasto-plasticity. SIAM J. Math. Anal. 40 (2008) 623–652. [CrossRef] [MathSciNet] [Google Scholar]
  40. U. Stefanelli, The discrete Brezis-Ekeland principle. J. Convex Anal. 16 (2009) 71–87. [MathSciNet] [Google Scholar]
  41. L. Tartar, Théorème d'interpolation non linéaire et applications. C. R. Acad. Sci. Paris Sér. A-B 270 (1970) A1729–A1731. [Google Scholar]
  42. L. Tartar, Interpolation non linéaire et régularité. J. Funct. Anal. 9 (1972) 469–489. [CrossRef] [Google Scholar]
  43. H. Triebel, Interpolation theory, function spaces, differential operators. Second edition, Johann Ambrosius Barth, Heidelberg, Germany (1995). [Google Scholar]
  44. A. Visintin, A new approach to evolution. C. R. Acad. Sci. Paris Sér. I Math. 332 (2001) 233–238. [Google Scholar]
  45. A. Visintin, An extension of the Brezis-Ekeland-Nayroles principle to monotone operators. Adv. Math. Sci. Appl. 18 (2008) 633–650. [MathSciNet] [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.