Free Access
Issue |
ESAIM: COCV
Volume 17, Number 3, July-September 2011
|
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Page(s) | 603 - 647 | |
DOI | https://doi.org/10.1051/cocv/2010018 | |
Published online | 23 April 2010 |
- R. Adams, Sobolev Spaces. Academic Press (1975). [Google Scholar]
- G. Alberti, G. Bouchitté and P. Seppecher, Phase transition with the line tension effect. Arch. Rational Mech. Anal. 144 (1998) 1–46. [CrossRef] [MathSciNet] [Google Scholar]
- L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Clarendon Press, Oxford (2000). [Google Scholar]
- J. Ball, A version of the fundamental theorem for Young measures, in PDEs and continuum models of phase transitions (Nice, 1988), Lecture Notes in Phys. 344, Springer, Berlin (1989) 207–215. [Google Scholar]
- R. Choksi and R. Kohn, Bounds on the micromagnetic energy of a uniaxial ferromagnet. Comm. Pure Appl. Math. 51 (1998) 259–289. [CrossRef] [MathSciNet] [Google Scholar]
- R. Choksi, R. Kohn and F. Otto, Domain branching in uniaxial ferromagnets: a scaling law for the minimum energy. Comm. Math. Phys. 201 (1999) 61–79. [CrossRef] [MathSciNet] [Google Scholar]
- R. Choksi, R. Kohn and F. Otto, Energy minimization and flux domain structure in the intermediate state of a type-I superconductor. J. Nonlinear Sci. 14 (2004) 119–171. [CrossRef] [MathSciNet] [Google Scholar]
- R. Choksi, S. Conti, R. Kohn and F. Otto, Ground state energy scaling laws during the onset and destruction of the intermediate state in a type I superconductor. Comm. Pure Appl. Math. 61 (2008) 595–626. [CrossRef] [MathSciNet] [Google Scholar]
- S. Conti, I. Fonseca and G. Leoni, A Γ-convergence result for the two-gradient theory of phase transitions. Comm. Pure Applied Math. 55 (2002) 857–936. [Google Scholar]
- G. Dal Maso, An Introduction to Γ-Convergence. Birkhäuser (1993). [Google Scholar]
- E. DiBenedetto, Real Analysis. Birkhäuser (2002). [Google Scholar]
- L. Evans and R. Gariepy, Measure Theory and fine Properties of Functions. CRC Press (1992). [Google Scholar]
- I. Fonseca and G. Leoni, Modern methods in the calculus of variations: Lp spaces, Springer Monographs in Mathematics. Springer (2007). [Google Scholar]
- I. Fonseca and C. Mantegazza, Second order singular perturbation models for phase transitions. SIAM J. Math. Anal. 31 (2000) 1121–1143. [CrossRef] [MathSciNet] [Google Scholar]
- E. Gagliardo, Ulteriori prorietà di alcune classi di funzioni in più variabili. Ric. Mat. 8 (1959) 24–51. [Google Scholar]
- A. Garroni and G. Palatucci, A singular perturbation result with a fractional norm, in Variational problems in materials science, Progr. Nonlinear Differential Equations Appl. 68, Birkhäuser, Basel (2006) 111–126. [Google Scholar]
- E. Giusti, Minimal Surfaces and Functions of Bounded Variation. Birkhäuser (1984). [Google Scholar]
- E. Hebey, Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities. AMS/CIMS (1999). [Google Scholar]
- M. Miranda, D. Pallara, F. Paronetto and M. Preunkert, Heat semigroup and functions of bounded variation on Riemannian manifolds. J. Reine Angew. Math. 613 (2007) 99–119. [CrossRef] [MathSciNet] [Google Scholar]
- L. Modica, The gradient theory of phase transitions and the minimal interface criterion. Arch. Rational Mech. Anal. 98 (1987) 123–142. [CrossRef] [MathSciNet] [Google Scholar]
- L. Modica, The gradient theory of phase transitions with boundary contact energy. Ann. Inst. Henri Poincaré, Anal. non linéaire 4 (1987) 487–512. [Google Scholar]
- L. Modica and S. Mortola, Un esempio de Γ--convergenza. Boll. Un. Mat. Ital. B 14 (1977) 285–299. [MathSciNet] [Google Scholar]
- S. Müller, Variational models for microstructure and phase transitions, in Calculus of variations and geometric evolution problems (Cetraro, 1996), Lecture Notes in Math. 1713, Springer (1999) 85–210. [Google Scholar]
- L. Nirenberg, An extended interpolation inequality. Ann. Sc. Normale Pisa - Scienze fisiche e matematiche 20 (1966) 733–737. [Google Scholar]
- E. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton University Press (1970). [Google Scholar]
- L. Tartar, Compensated compactness and applications to partial differential equations, in Nonlinear analysis and mechanics: Heriot-Watt Symposium IV, Res. Notes in Math. 39, Pitman, Boston (1979) 136–212. [Google Scholar]
- W. Ziemer, Weakly differentiable functions – Sobolev spaces and functions of bounded variation, Graduate Texts in Mathematics 120. Springer-Verlag, New York (1989). [Google Scholar]
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