Open Access
Issue
ESAIM: COCV
Volume 26, 2020
Article Number 89
Number of page(s) 34
DOI https://doi.org/10.1051/cocv/2020010
Published online 13 November 2020
  1. H.W. Alt and L.A. Caffarelli, Existence and regularity for a minimum problem with free boundary. J. Reine Angew. Math. 325 (1981) 105–144. [MathSciNet] [Google Scholar]
  2. H.W. Alt, L.A. Caffarelli and A. Friedman, Variational problems with two phases and their free boundary. Trans. Am. Math. Soc. 282 (1984) 431–461. [Google Scholar]
  3. T. Briançon, M. Hayouni and M. Pierre, Lipschitz continuity of state functions in some optimal shaping. Calc. Var. Partial Differ. Equ. 23 (2005) 13–32. [Google Scholar]
  4. D. Bucur, D. Mazzoleni, A. Pratelli and B. Velichkov, Lipschitz regularity of the eigenfunctions on optimal domains. Arch. Ration. Mech. Anal. 216 (2015) 117–151. [Google Scholar]
  5. L.A. Caffarelli, D. Jerison and C.E. Kenig, Global energy minimizers for free boundary problems and full regularity in three dimensions. In Noncompact problems at the intersection of geometry, analysis, and topology. Proceedings of the conference on noncompact variational problems and general relativity held in honor of Haim Brezis and Felix Browder at Rutgers University, New Brunswick, NJ, USA, October 14–18, 2001. American Mathematical Society (AMS), Providence, RI (2004) 83–97. [Google Scholar]
  6. G. David and T. Toro, Regularity of almost minimizers with free boundary. Calc. Variat. Partial Differ. Equ. 54 (2015) 455–524. [CrossRef] [Google Scholar]
  7. G. David, M. Engelstein, M. Smit Vega Garcia and T. Toro, Regularity for almost-minimizers of variable coefficient Bernoulli-type functional. Preprint arXiv:1909.05043 (2019). [Google Scholar]
  8. G. David, M. Engelstein and T. Toro, Free boundary regularity for almost-minimizers. Adv. Math. 350 (2019) 1109–1192. [CrossRef] [Google Scholar]
  9. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Reprint ofthe 1998. Springer (Berlin), (2001). [Google Scholar]
  10. A. Henrot and M. Pierre, Variation et optimisation de formes. Une analyse géométrique, vol. 48. Springer, Berlin (2005). [Google Scholar]
  11. J. Lamboley and P. Sicbaldi, Existence and regularity of Faber Krahn minimizers in a Riemannian manifold. Preprint arXiv:1907.08159 (2019). [Google Scholar]
  12. F. Maggi, Sets of finite perimeter and geometric variational problems. An introduction to geometric measure theory, vol. 135. Cambridge University Press, Cambridge (2012). [Google Scholar]
  13. N. Matevosyan and A. Petrosyan, Almost monotonicity formulas for elliptic and parabolic operators with variable coefficients. Commun. Pure Appl. Math. 64 (2011) 271–311. [Google Scholar]
  14. D. Mazzoleni, S. Terracini and B. Velichkov, Regularity of the optimal sets for some spectral functionals. Geom. Funct. Anal. 27 (2017) 373–426. [CrossRef] [Google Scholar]
  15. E. Russ, B. Trey and B. Velichkov, Existence and regularity of optimal shapes for elliptic operators with drift. Calc. Variat. Part. Differ. Equ. 58 (2019) 199. [CrossRef] [Google Scholar]
  16. L. Spolaor, B. Trey and B. Velichkov, Free boundary regularity for a multiphase shape optimization problem. Commun. Partial Differ. Equ. (2019) 1–32. [Google Scholar]
  17. B. Trey, Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form. Preprint arXiv:2001.06504 (2020). [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.