Free Access
Volume 19, Number 3, July-September 2013
Page(s) 740 - 753
Published online 03 June 2013
  1. G. Bellettini, G. Dal Maso and M. Paolini, Semicontinuity and relaxation properties of a curvature depending functional in 2d. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 20 (1993) 247–297. [MathSciNet] [Google Scholar]
  2. G. Bellettini and L. Mugnai, A varifolds representation of the relaxed elastica functional. J. Convex Anal. 14 (2007) 543–564. [Google Scholar]
  3. G. Bellettini and L. Mugnai, Approximation of Helfrich’s functional via diffuse interfaces. SIAM J. Math. Anal. 42 (2010) 2402–2433. [CrossRef] [MathSciNet] [Google Scholar]
  4. G. Bellettini and M. Paolini, Approssimazione variazionale di funzionali con curvatura. Seminario Analisi Matematica Univ. Bologna (1993). [Google Scholar]
  5. A. Braides and R. March, Approximation by Γ-convergence of a curvature-depending functional in visual reconstruction. Commun. Pure Appl. Math. 59 (2006) 71–121. [CrossRef] [MathSciNet] [Google Scholar]
  6. X. Cabré and J. Terra, Saddle-shaped solutions of bistable diffusion equations in all of R2m. J. Eur. Math. Soc. 43 (2009) 819–943. [CrossRef] [Google Scholar]
  7. G. Dal Maso, An introduction to Γ-convergence, vol. 8, Progress in Nonlinear Differential Equations and their Applications. Birkhäuser, Boston, MA (1993). [Google Scholar]
  8. H. Dang, P. Fife and L. Peletier, Saddle solutions of the bistable diffusion equation. Z. Angew. Math. Phys. 43 (1992) 984–998. [CrossRef] [MathSciNet] [Google Scholar]
  9. E. De Giorgi, Some remarks on Γ-convergence and least squares method, in Composite media and homogenization theory (Trieste, 1990), MA. Progr. Nonlinear Differ. Eq. Appl. 5 (1991) 135–142. [Google Scholar]
  10. P. Dondl, L. Mugnai and M. Röger, Confined elastic curves. SIAM J. Appl. Math. 71 (2011) 2205–2226. [CrossRef] [MathSciNet] [Google Scholar]
  11. Q. Du, C. Liu, R. Ryham and X. Wang, A phase field formulation of the Willmore problem. Nonlinearity 18 (2005) 1249–1267. [CrossRef] [Google Scholar]
  12. Q. Du, C. Liu and X. Wang, A phase field approach in the numerical study of the elastic bending energy for vesicle membranes. J. Comput. Phys. 198 (2004) 450–468. [CrossRef] [MathSciNet] [Google Scholar]
  13. J. Hutchinson, C1, α-multiple function regularity and tangent cone behavior for varifolds with second fundamental form in Lp, in Geometric measure theory and the calculus of variations (Arcata, Calif., 1984). Proc. Sympos. Pure Math. Amer. Math. Soc. 44 (1984) 281–306. [CrossRef] [Google Scholar]
  14. J. Hutchinson, Second fundamental form for varifolds and the existence of surfaces minimising curvature. Indiana Univ. Math. J. 35 (1986) 281–306. [Google Scholar]
  15. J.S. Lowengrub, A. Rätz and A. Voigt, Phase-field modeling of the dynamics of multicomponent vesicles: spinodal decomposition, coarsening, budding, and fission. Phys. Rev. E 79 (2009) 82C99–92C10. [Google Scholar]
  16. L. Modica and S. Mortola, Un esempio di Γ-convergenza. Boll. Un. Mat. Ital. B 14 (1977) 285–299. [MathSciNet] [Google Scholar]
  17. Y. Nagase and Y. Tonegawa, A singular perturbation problem with integral curvature bound. Hiroshima Math. Journal 37 (2007) 455–489. [Google Scholar]
  18. M. Röger and R. Schätzle. On a modified conjecture of De Giorgi. Math. Z. 254 (2006) 675–714. [CrossRef] [MathSciNet] [Google Scholar]
  19. L. Simon, Proceedings of the Centre for Mathematical Analysis, Australian National University. Centre for Math. Anal., Lectures on Geometric Measure Theory, vol. 3. Australian National Univ., Canberra (1984). [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.