Free Access
Issue |
ESAIM: COCV
Volume 12, Number 3, July 2006
|
|
---|---|---|
Page(s) | 564 - 614 | |
DOI | https://doi.org/10.1051/cocv:2006013 | |
Published online | 20 June 2006 |
- L. Ambrosio, Minimizing movements. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. 19 (1995) 191–246. [MathSciNet] [Google Scholar]
- L. Ambrosio, N. Fusco and D. Pallara, Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs, Clarendon Press, Oxford (2000). [Google Scholar]
- 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 (2005). [Google Scholar]
- C. Baiocchi, Discretization of evolution variational inequalities, Partial differential equations and the calculus of variations, Vol. I, F. Colombini, A. Marino, L. Modica and S. Spagnolo, Eds., Birkhäuser Boston, Boston, MA (1989) 59–92. [Google Scholar]
- E.J. Balder, A general approach to lower semicontinuity and lower closure in optimal control theory. SIAM J. Control Optim. 22 (1984) 570–598. [CrossRef] [MathSciNet] [Google Scholar]
- E.J. Balder, An extension of Prohorov's theorem for transition probabilities with applications to infinite-dimensional lower closure problems. Rend. Circ. Mat. Palermo 34 (1985) 427–447. [CrossRef] [MathSciNet] [Google Scholar]
- E.J. Balder, Lectures on Young measure theory and its applications in economics. Rend. Istit. Mat. Univ. Trieste 31 (2000) (Suppl. 1), 1–69, Workshop on Measure Theory and Real Analysis (Italian) (Grado, 1997). [Google Scholar]
- J.M. Ball, A version of the fundamental theorem for Young measures, PDEs and continuum models of phase transitions (Nice 1988), Springer, Berlin. Lect. Notes Phys. 344 (1989) 207–215. [Google Scholar]
- G. Bouchitté, Singular perturbations of variational problems arising from a two-phase transition model. Appl. Math. Optim. 21 (1990) 289–314. [CrossRef] [MathSciNet] [Google Scholar]
- A. Bressan, A. Cellina and G. Colombo, Upper semicontinuous differential inclusions without convexity. Proc. Amer. Math. Soc. 106 (1989) 771–775. [MathSciNet] [Google Scholar]
- H. Brézis, Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, Contribution to Nonlinear Functional Analysis, in Proc. Sympos. Math. Res. Center, Univ. Wisconsin, Madison, 1971. Academic Press, New York (1971) 101–156. [Google Scholar]
- H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Publishing Co., Amsterdam (1973), North-Holland Mathematics Studies, No. 5. Notas de Matemática (50). [Google Scholar]
- H. Brézis, Analyse fonctionnelle - Théorie et applications. Masson, Paris (1983). [Google Scholar]
- H. Brézis, On some degenerate nonlinear parabolic equations, Nonlinear Functional Analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 1, Chicago, Ill., 1968), Providence, R.I., Amer. Math. Soc. (1970) 28–38. [Google Scholar]
- T. Cardinali, G. Colombo, F. Papalini and M. Tosques, On a class of evolution equations without convexity. Nonlinear Anal. 28 (1997) 217–234. [CrossRef] [MathSciNet] [Google Scholar]
- C. Castaing and M. Valadier, Convex analysis and measurable multifunctions. Springer, Berlin-New York (1977). [Google Scholar]
- M.G. Crandall and T.M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces. Amer. J. Math. 93 (1971) 265–298. [CrossRef] [MathSciNet] [Google Scholar]
- M.G. Crandall and A. Pazy, Semi-groups of nonlinear contractions and dissipative sets. J. Functional Anal. 3 (1969) 376–418. [CrossRef] [Google Scholar]
- E. De Giorgi, New problems on minimizing movements, Boundary Value Problems for PDE and Applications, C. Baiocchi and J.L. Lions, Eds., Masson (1993) 81–98. [Google Scholar]
- E. De Giorgi, A. Marino and M. Tosques, Problems of evolution in metric spaces and maximal decreasing curve. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 68 (1980) 180–187. [MathSciNet] [Google Scholar]
- C. Dellacherie and P.A. Meyer, Probabilities and potential. North-Holland Publishing Co., Amsterdam (1978). [Google Scholar]
- R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998) 1–17 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
- T. Kato, Perturbation theory for linear operators. Springer, Berlin (1976). [Google Scholar]
- Y. Kōmura, Nonlinear semi-groups in Hilbert space. J. Math. Soc. Japan 19 (1967) 493–507. [CrossRef] [MathSciNet] [Google Scholar]
- A.Ja. Kruger and B.Sh. Mordukhovich, Extremal points and the Euler equation in nonsmooth optimization problems. Dokl. Akad. Nauk BSSR 24 (1980) 684–687, 763. [MathSciNet] [Google Scholar]
- S. Luckhaus, Solutions for the two-phase Stefan problem with the Gibbs-Thomson Law for the melting temperature. Euro. J. Appl. Math. 1 (1990) 101–111. [CrossRef] [Google Scholar]
- S. Luckhaus, The Stefan Problem with the Gibbs-Thomson law. Preprint No. 591 Università di Pisa (1991) 1–21. [Google Scholar]
- S. Luckhaus, The Gibbs-Thompson relation within the gradient theory of phase transitions. Arch. Rational Mech. Anal. 107 (1989) 71–83. [MathSciNet] [Google Scholar]
- 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]
- A. Mielke, F. Theil and V.I. Levitas, A variational formulation of rate-independent phase transformations using an extremum principle. Arch. Ration. Mech. Anal. 162 (2002) 137–177. [Google Scholar]
- L. Modica, Gradient theory of phase transitions and minimal interface criterion. Arch. Rational Mech. Anal. 98 (1986) 123–142. [Google Scholar]
-
L. Modica and S. Mortola, Un esempio di
-convergenza. Boll. Un. Mat. Ital. B 14 (1977) 285–299. [MathSciNet] [Google Scholar]
- B.Sh. Mordukhovich, Nonsmooth analysis with nonconvex generalized differentials and conjugate mappings. Dokl. Akad. Nauk BSSR 28 (1984) 976–979. [MathSciNet] [Google Scholar]
- R.H. Nochetto, G. Savaré and C. Verdi, A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations. Comm. Pure Appl. Math. 53 (2000) 525–589. [CrossRef] [MathSciNet] [Google Scholar]
- P.I. Plotnikov and V.N. Starovoitov, The Stefan problem with surface tension as the limit of a phase field model. Differential Equations 29 (1993) 395–404. [MathSciNet] [Google Scholar]
- R.T. Rockafellar, Convex analysis. Princeton University Press, Princeton (1970). [Google Scholar]
- R.T. Rockafellar and R.J.B. Wets, Variational analysis. Springer-Verlag, Berlin (1998). [Google Scholar]
- R. Rossi and G. Savaré, Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces. Ann. Sc. Norm. Sup., Pisa 2 (2003) 395–431. [Google Scholar]
- R. Rossi and G. Savaré, Existence and approximation results for gradient flows. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (9) Mat. Appl. 15 (2004) 183–196. [Google Scholar]
- J. Rulla, Error analysis for implicit approximations to solutions to Cauchy problems. SIAM J. Numer. Anal. 33 (1996) 68–87. [CrossRef] [MathSciNet] [Google Scholar]
- G. Savaré, Weak solutions and maximal regularity for abstract evolution inequalities. Adv. Math. Sci. Appl. 6 (1996) 377–418. [MathSciNet] [Google Scholar]
- G. Savaré, Compactness properties for families of quasistationary solutions of some evolution equations. Trans. Amer. Math. Soc. 354 (2002) 3703–3722. [CrossRef] [MathSciNet] [Google Scholar]
- R. Schätzle, The quasistationary phase field equations with Neumann boundary conditions. J. Differential Equations 162 (2000) 473–503. [CrossRef] [MathSciNet] [Google Scholar]
- L. Simon, Lectures on geometric measure theory, in Proc. Centre for Math. Anal., Australian Nat. Univ. 3 (1983). [Google Scholar]
- M. Valadier, Young measures, Methods of nonconvex analysis (Varenna, 1989). Springer, Berlin (1990) 152–188. [Google Scholar]
- A. Visintin, Differential models of hysteresis. Appl. Math. Sci. 111, Springer-Verlag, Berlin (1994). [Google Scholar]
- A. Visintin, Models of phase transitions. Progress in Nonlinear Differential Equations and Their Applications 28, Birkhäuser, Boston (1996). [Google Scholar]
- A. Visintin, Forward-backward parabolic equations and hysteresis. Calc. Var. Partial Differential Equations 15 (2002) 115–132. [CrossRef] [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.