Open Access
Issue
ESAIM: COCV
Volume 28, 2022
Article Number 50
Number of page(s) 39
DOI https://doi.org/10.1051/cocv/2022045
Published online 20 July 2022
  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. [CrossRef] [Google Scholar]
  2. 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]
  3. 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). xviii–434 pp. [Google Scholar]
  4. G. Anzellotti, Pairings between measures and bounded functions and compensated compactness. Ann. Mat. Pura Appl. (4) 135 (1984) 293–318. [Google Scholar]
  5. H. Bischof, A. Chambolle, D. Cremers and T. Pock, An algorithm for minimizing the Mumford-Shah functional. 2009 IEEE 12th International Conference on Computer Vision (2009). [Google Scholar]
  6. B. Bogosel and M. Foare, Numerical implementation in 1D and 2D of a shape optimization problem with Robin boundary conditions. Preprint http://www.cmap.polytechnique.fr/~beniamin.bogosel/pdfs/Robin.pdf. [Google Scholar]
  7. G. Bouchitte and I. Fragalá, A duality theory for non-convex problems in the calculus of variations. Arch. Rati. Mech. Anal. 229 (2018) 361–415. [CrossRef] [Google Scholar]
  8. D. Bucur, G. Buttazzo and C. Nitsch, Two optimization problems in thermal insulation. Notices Amer. Math. Soc. 64 (2017) 830–835. [CrossRef] [MathSciNet] [Google Scholar]
  9. D. Bucur, G. Buttazzo and C. Nitsch, Symmetry breaking for a problem in optimal insulation. J. Math. Pures Appl. (9) 107 (2017) 451–463. [CrossRef] [MathSciNet] [Google Scholar]
  10. D. Bucur and A. Giacomini, Shape optimization problems with Robin conditions on the free boundary. Ann. Inst. H. Poincare Anal. Non Linéaire 33 (2016) 1539–1568. [CrossRef] [MathSciNet] [Google Scholar]
  11. D. Bucur and S. Luckhaus, Monotonicity formula and regularity for general free discontinuity problems. Arch. Ratl. Mech. Anal. 211 (2014) 489–511. [CrossRef] [Google Scholar]
  12. D. Bucur, M. Nahon, C. Nitsch and C. Trombetti, Shape optimization of a thermal insulation problem. Preprint available at https://arxiv.org/abs/2112.07300. [Google Scholar]
  13. G. Buttazzo, An optimization problem for thin insulating layers around a conducting medium. Boundary control and boundary variations (Nice, 1986). Lecture Notes in Comput. Sci., 100, Springer, Berlin (1988) 91–95. [CrossRef] [Google Scholar]
  14. L.A. Caffarelli and D. Kriventsov, A free boundary problem related to thermal insulation. Comm.. Partial Differ. Equ. 41 (2016) 1149–1182. [CrossRef] [Google Scholar]
  15. A. Chambolle, Convex representation for lower semicontinuous envelopes of functionals in L1. J. Convex Anal. 8 (2001) 149–170. [MathSciNet] [Google Scholar]
  16. A. Chambolle, D. Cremers and E. Strekalovskiy, A Convex, Representation for the Vectorial Mumford-Shah Functional, in IEEE Conference on Computer Vision and Pattern Recognition (2012). [Google Scholar]
  17. A. Chambolle, V. Duval, G. Peyráe and C. Poon, Geometric properties of solutions to the total variation denoising problem. Inverse Probl. 33 (2017) 015002, 44 pp. [CrossRef] [Google Scholar]
  18. A. Chambolle and M. Novaga, Anisotropic and crystalline mean curvature flow of mean-convex sets. Annali Scuola Normale Superiore - Classe di Scienze (2021), p. 17. [Google Scholar]
  19. G. Dal Maso, M.G. Mora and M. Morini, Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets. J. Math. Pures Appl. (9) 79 (2000) 141–162. [CrossRef] [MathSciNet] [Google Scholar]
  20. T. De Pauw and D. Smets, On explicit solutions for the problem of Mumford and Shah. Commun. Contemp. Math. 1 (1999) 201–212. [CrossRef] [Google Scholar]
  21. G.B. Folland, Introduction to partial differential equations. Second edition. Princeton University Press, Princeton, NJ (1995). xii+324, pp. [Google Scholar]
  22. N. Fusco, An overview of the Mumford-Shah problem. Milan J. Math. 71 (2003) 95–119. [CrossRef] [MathSciNet] [Google Scholar]
  23. D. Kriventsov, A free boundary problem related to thermal insulation: flat implies smooth. Calc. Var. Partial Differ. Equ. 58 (2019) Paper No. 78, 83 pp. [CrossRef] [Google Scholar]
  24. C. Labourie and E. Milakis, Higher integrability of the gradient for the Thermal Insulation problem. Preprint available at arXiv:2101.09692. [Google Scholar]
  25. F. Maggi, Sets of finite perimeter and geometric variational problems. An introduction to geometric measure theory. Cambridge Studies in Advanced Mathematics, 135. Cambridge University Press, Cambridge (2012). xx+454 pp. [Google Scholar]
  26. M.G. Mora, Local calibrations for minimizers of the Mumford-Shah functional with a triple junction. Commun. Contemp. Math. 4 (2002) 297–326. [CrossRef] [Google Scholar]
  27. M.G. Mora and M. Morini, Local calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set. Ann. Inst. H. Poincare Anal. Non Linaire 18 (2001) 403–436. [CrossRef] [Google Scholar]
  28. M. Morini, Global calibrations for the non-homogeneous Mumford-Shah functional. Ann. Sci. Norm. Super. Pisa CI. Sci. (5) 1 (2002) 603–648. [Google Scholar]
  29. C. Scheven and T. Schmidt, BV supersolutions to equations of 1-Laplace and minimal surface type. J. Differ. Equ. 261 (2016) 1904–1932. [CrossRef] [Google Scholar]

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