On a modified conjecture of De Giorgi

Mathematische Zeitschrift

Volumn 254, Issue 4, 2006, Pages 675-714

  Röger, Matthias ^a   Schätzle, Reiner ^b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

limit; Cahn Hilliard theory; Geometric measure theory; Willmore functional

Indexed keywords

EID: 33749607402     PISSN: 00255874     EISSN: 14321823     Source Type: Journal    
DOI: 10.1007/s00209-006-0002-6     Document Type: Article

References (15)

1. Allard, W.K.: On the first variation of a varifold. Ann. Math. 95, 417-491 (1972)
2. Bellettini, G., Mugnai, L.: On the approximation of the elastica functional in radial symmetry. Cal. Var. Partial Differential Equations 24(1), 1-20 (2005)
3. Bellettini, G., Paolini, M.: Approssimazione variazionale di funzionali con curvatura. Seminario di Analisi Matematica, Dipartimento di Matematica dell'Università di Bologna. Tecnoprint Bologna, 87-97 (1993)
4. Chen, X.: Global asymptotic limit of solutions of the Cahn-Hilliard equation. J Differential Geom. 44(2), 262-311 (1996)
5. de Giorgi, E.: Some remarks on Γ-convergence and least squares methods. In: Dal Maso, G., Dell'Antonio, G.F. (eds), Composite Media Homogenization Theory Progress in Nonlinear Differential Equations and their Applications, vol. 5, Birkhäuser, 135-142 (1991)
6. Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Springer, Berlin Heidelberg New York (1998)
7. Hutchinson, J., Tonegawa, Y.: Convergence of phase interfaces in the van der Waals-Cahn-Hilliard Theory. Cal. Var. Partial Differential Equations 10(1), 49-84 (2000)
8. Loreti, P., March, R.: Propagation of fronts in a nonlinear fourth order equation. Eur. J App. Math. 11, 203-213 (2000)
9. Modica, L., Mortola, S.: Un esempio di Γ-convergenza. Bollettino della Unione Matematica Italiana, vol. 14B, 285-299 (1977)
10. Modica, L.: The gradient theory of phase transitions and the minimal interface criterion. Arch. Ration. Mech. Anal. 98(2), 123-142 (1987)
11. Moser, R.: A higher order asymptotic problem related to phase transitions. SIAM J. Math. Anal. 37, 712-736 (2004)
12. Padilla, P., Tonegawa, Y.: On the convergence of stable phase transitions. Commun. Pure Appl. Math. 51(6), 551-579 (1998)
13. Schätzle, R.: Lower semicontinuity of the Willmore functional for currents (2004) (submitted)
14. Simon, L.: Lectures on geometric measure theory. In: Proceedings of the Centre for Mathematical Analysis Australian National University, vol 3 (1983)
15. Tonegawa, Y.: Phase field model with a variable chemical potential, Proc. Roy. Soc. Edinburgh, Sect. A, 132(4), 993-1019 (2002)