Open Access
Issue
ESAIM: COCV
Volume 27, 2021
Article Number 35
Number of page(s) 51
DOI https://doi.org/10.1051/cocv/2021035
Published online 30 April 2021
  1. D.R. Adams and L.I. Hedberg, Function spaces and potential theory. Vol. 314 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin (1996). [CrossRef] [Google Scholar]
  2. 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]
  3. J.-F. Babadjian, F. Iurlano and A. Lemenant, Partial regularity for the crack set minimizing the two-dimensional Griffith energy. To appear in J. Eur. Math. Soc. (JEMS) (2020). [Google Scholar]
  4. T. Bagby, Quasi topologies and rational approximation. J. Funct. Anal. 10 (1972) 259–268. [Google Scholar]
  5. A. Bonnet, On the regularity of edges in image segmentation. Ann. Inst. Henri Poincaré Anal. Non Linéaire 13 (1996) 485–528. [Google Scholar]
  6. M. Bonnivard, A. Lemenant and F. Santambrogio, Approximation of length minimization problems among compact connected sets. SIAM J. Math. Anal. 47 (2015) 1489–1529. [Google Scholar]
  7. D. Bucur and P. Trebeschi, Shape optimisation problems governed by nonlinear state equations. Proc. Roy. Soc. Edinburgh Sect. A 128 (1998) 945–963. [Google Scholar]
  8. G. Buttazzo, E. Oudet and E. Stepanov, Optimal transportation problems with free Dirichlet regions. Progr. Nonlinear Differ. Equ. Appl. 51 (2002) 41–65. [Google Scholar]
  9. G. Buttazzo and F. Santambrogio, Asymptotical compliance optimization for connected networks. Netw. Heterog. Media 2 (2007) 761–777. [CrossRef] [MathSciNet] [Google Scholar]
  10. G. Buttazzo and E. Stepanov, Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem. Ann. Sc. Norm. Super. Pisa Cl. Sci. 2 (2003) 631–678. [Google Scholar]
  11. A. Chambolle, J. Lamboley, A. Lemenant and E. Stepanov, Regularity for the optimal compliance problem with length penalization. SIAM J. Math. Anal. 49 (2017) 1166–1224. [Google Scholar]
  12. G. Dal Maso and F. Murat, Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 24 (1997). [Google Scholar]
  13. G. David, Singular sets of minimizers for the Mumford-Shah functional. Vol. 233 of Progress in mathematics. Birkhäuser-Verlag, Basel (2005). [Google Scholar]
  14. G. David and S. Semmes, Analysis of and on uniformly rectifiable sets. Vol. 38 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (1993). [CrossRef] [Google Scholar]
  15. E. DiBenedetto, C1+α local regularity of weak solutions of degenerate elliptic equations. Nonlinear Anal. 7 (1983) 827–850. [Google Scholar]
  16. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. Textbooks in Mathematics. CRC Press, Boca Raton, FL, revised edition (2015). [Google Scholar]
  17. H. Federer, Geometric measure theory. Die Grundlehren der mathematischen Wissenschaften, Band 153. Springer-Verlag New York Inc., New York (1969). [Google Scholar]
  18. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Vol. 224 of Grundlehren der mathematischen Wissenschaften. Springer-Verlag, Berlin, second edition (2001). [Google Scholar]
  19. L.I. Hedberg, Non-linear potentials and approximation in the mean by analytic functions. Math. Z. 129 (1972) 299–319. [Google Scholar]
  20. K. Kuratowski, Topologie. I et II. Éditions Jacques Gabay, Sceaux. Part I with an appendix by A. Mostowski and R. Sikorski, Reprint of the fourth (Part I) and third (Part II) editions (1992). [Google Scholar]
  21. P. Lindqvist, Notes on the stationary p-Laplace equation. Springer Briefs in Mathematics. Springer, Cham (2019). [Google Scholar]
  22. A. Nayam, Asymptotics of an optimal compliance-network problem. Netw. Heterog. Media 8 (2013) 573–589. [Google Scholar]
  23. A. Nayam, Constant in two-dimensional p-compliance-network problem. Netw. Heterog. Media 9 (2014) 161–168. [Google Scholar]
  24. E. Paolini and E. Stepanov, Existence and regularity results for the Steiner problem. Calc. Var. Partial Differ. Equ. 46 (2013) 837–860. [Google Scholar]
  25. D. Slepčev, Counterexample to regularity in average-distance problem. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014) 169–184. [Google Scholar]
  26. V. Šverák On optimal shape design. J. Math. Pures Appl. 72 (1993) 537–551. [Google Scholar]
  27. W.P. Ziemer, Weakly differentiable functions. Sobolev spaces and functions of bounded variation. Vol. 120 of Graduate Texts in Mathematics. Springer-Verlag, New York (1989). [CrossRef] [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.