Free Access
Volume 26, 2020
Article Number 40
Number of page(s) 28
Published online 30 June 2020
  1. G. Alberti, G. Bouchitté and G. Dal Maso The calibration method for the Mumford-Shah functional and free-discontinuity problems. Calc. Var. Partial Differ. Equ. 16 (2003) 299–333. [Google Scholar]
  2. S. Amato, G. Bellettini and M. Paolini, Constrained BV functions on covering spaces for minimal networks and Plateau’s type problems. Adv. Calc. Var. 10 (2017) 25–47. [CrossRef] [Google Scholar]
  3. L. Ambrosio and A. Braides, Functionals defined on partitions in sets of finite perimeter. I. Integral representation and Γ-convergence. J. Math. Pures Appl. 69 (1990) 285–305. [Google Scholar]
  4. L. Ambrosio and A. Braides, Functionals defined on partitions in sets of finite perimeter. II. Semicontinuity, relaxation and homogenization. J. Math. Pures Appl. 69 (1990) 307–333. [Google Scholar]
  5. L. Ambrosio, V. Caselles, S. Masnou and J.-M. Morel, Connected components of sets of finite perimeter and applications to image processing. J. Eur. Math. Soc. (JEMS) 3 (2001) 39–92. [CrossRef] [MathSciNet] [Google Scholar]
  6. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York (2000). [Google Scholar]
  7. G. Bellettini, M. Paolini and F. Pasquarelli, Triple covers and a non-simply connected surface spanning an elongated tetrahedron and beating the cone. Interfaces Free Bound. 20 (2018) 407–436. [CrossRef] [Google Scholar]
  8. G. Bellettini, M. Paolini, F. Pasquarelli and G. Scianna, Covers, soap films and BV functions. Geom. Flows 3 (2018) 57–75. [CrossRef] [Google Scholar]
  9. G. Bellettini, M. Paolini and C. Verdi, Numerical minimization of geometrical type problems related to calculus of variations. Calcolo 27 (1990) 251–278. [CrossRef] [Google Scholar]
  10. M. Bonafini, Convex relaxation and variational approximation of the steiner problem: theory and numerics, Geom. Flows 3 (2018) 19–27. [CrossRef] [Google Scholar]
  11. M. Bonafini, G. Orlandi and E. Oudet, Variational approximation of functionals defined on 1-dimensional connected sets: the planar case. SIAM J. Math. Anal. 50 (2018) 6307–6332. [CrossRef] [Google Scholar]
  12. M. Bonnivard, A. Lemenant and F. Santambrogio, Approximation of length minimization problems among compact connected sets. SIAM J. Math. Anal. 47 (2015) 1489–1529. [CrossRef] [Google Scholar]
  13. K.A. Brakke, Numerical solution of soap film dual problems. Exp. Math. 4 (1995) 269–287. [Google Scholar]
  14. K.A. Brakke, Soap films and covering spaces. J. Geom. Anal. 5 (1995) 445–514. [Google Scholar]
  15. M. Carioni and A. Pluda, On different notions of calibrations for minimal partitions and minimal networks in ℝ2. Preprint arxiv:1805.11397; To appear in Adv. Calc. Var. (2019). doi: 10.1515/acv-2019-0005. [Google Scholar]
  16. A. Chambolle, L.A.D. Ferrari and B. Merlet, A phase-field approximation of the Steiner problem in dimension two. Adv. Calc. Var. 12 (2019) 157–173. [CrossRef] [Google Scholar]
  17. R. Courant and H. Robbins, What Is Mathematics? Oxford University Press, New York (1941). [Google Scholar]
  18. D.Z. Du, F.K. Hwang and J.F. Weng, Steiner minimal trees for regular polygons. Discrete Comput. Geom. 2 (1987) 65–84. [Google Scholar]
  19. J.H.G. Fu, Tubular neighborhoods in Euclidean spaces. Duke Math. J. 52 (1985) 1025–1046. [CrossRef] [MathSciNet] [Google Scholar]
  20. A.O. Ivanov and A.A. Tuzhilin, Minimal Networks: The Steiner Problem and Its Generalizations. CRC Press, Boca Raton FL (1994). [Google Scholar]
  21. V. Jarník and M. Kössler, On minimal graphs containing n given points. Časopis Pěst. Mat. 63 (1934) 223–235. [Google Scholar]
  22. G. Lawlor and F. Morgan, Paired calibrations applied to soap films, immiscible fluids, and surfaces or networks minimizing other norms. Pac. J. Math. 166 (1994) 55–83. [CrossRef] [Google Scholar]
  23. A. Lemenant and F. Santambrogio, A Modica-Mortola approximation for the Steiner problem. C. R. Math. Acad. Sci. Paris 352 (2014) 451–454. [CrossRef] [Google Scholar]
  24. A. Marchese and A. Massaccesi, The Steiner tree problem revisited through rectifiable G-currents. Adv. Calc. Var. 9 (2016) 19–39. [Google Scholar]
  25. A. Massaccesi, E. Oudet and B. Velichkov, Numerical calibration of steiner trees. Appl. Math. Optim. 79 (2019) 69–86. [Google Scholar]
  26. J.-M. Morel and S. Solimini, Variational Methods in Image Segmentation: With Seven Image Processing Experiments. Vol. 14 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser Boston, Inc., Boston, MA (1995). [Google Scholar]
  27. E. Paolini and E. Stepanov, Existence and regularity results for the Steiner problem. Calc. Var. Partial Differ. Equ. 46 (2013) 837–860. [Google Scholar]
  28. I. Tamanini and G. Congedo, Density theorems for local minimizers of area-type functionals. Rend. Semin. Mat. Univ. Padova 85 (1991) 217–248. [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.