Partial regularity of free discontinuity sets, II

 Access to full text

 Full (PDF)

1. [1] L. Ambrosio, A compactness theorem for a new class of functions of bounded variation, Boll. Un. Mat. Ital.B3 (1989), 857-881. Zbl0767.49001MR1032614
2. [2] L. Ambrosio, Existence theory for a new class of variational problems, Arch. Rational Mech. Anal.111 (1990), 291-322. Zbl0711.49064MR1068374
3. [3] L. Ambrosio, Variational problems in SBV, Acta App. Math.17 (1989), 1-40. Zbl0697.49004MR1029833
4. [4] L. Ambrosio, A new proof of SBV compactness theorem, Calc. Var.3 (1995), 127-137. Zbl0837.49011MR1384840
5. [5] L. Ambrosio - D. Pallara, Partial regularity of free discontinuity sets I, Ann. Scuola Norm. Sup. Pisa Cl. Sci. ???. Zbl0896.49023
6. [6] A. Blake - A. Zisserman, Visual Reconstruction, M.I.T. Press, 1987. MR919733
7. [7] A. Bonnet, On the regularity of edges in the Mumford-Shah model for image segmentation, Ann. Inst. H. Poincaré, to appear. 
8. [8] M. Carriero - A. Leaci, Existence theorem for a Dirichlet problem with free discontinuity set, Nonlinear Analysis TMA15 (1990), 661-677. Zbl0713.49003MR1073957
9. [9] M. Carriero - A. Leaci - D. Pallara - E. Pascali, Euler Conditions for a Minimum Problem with Free Discontinuity Set, Preprint Dip. di Matematica, 8Lecce, 1988. 
10. [10] M. Carriero - A. Leaci - F. Tomarelli, Plastic free discontinuities and special bounded hessian, C.R. Acad. Sci. Paris Sér. I Math.314 (1992), 595-600. Zbl0794.49011MR1158743
11. [11] G. Dal Maso - J.M. Morel - S. Solimini, A variational method in image segmentation: existence and approximation results, Acta Math.168 (1992), 89-151. Zbl0772.49006MR1149865
12. [12] G. David - S. Semmes, On the singular set of minimizers of the Mumford-Shah functional, J. Math. Pures Appl. to appear. Zbl0853.49010
13. [13] G. David, C1-arcs for the minimizers of the Mumford- Shah functional, SIAM J. Appl. Math.56 (1996), 783-888. Zbl0870.49020MR1389754
14. [14] E. De Giorgi, Free Discontinuity Problems in Calculus of Variations, in: Frontiers in pure and applied Mathematics, a collection of papers dedicated to J.L. Lions on the occasion of his 60th birthday, R. Dautray ed., North Holland, 1991. Zbl0758.49002MR1110593
15. [15] E. De Giorgi - L. Ambrosio, Un nuovo tipo di funzionale del Calcolo delle Variazioni, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 82 (1988), 199-210. Zbl0715.49014MR1152641
16. [16] E. De Giorgi - M. Carriero - A. Leaci, Existence theorem for a minimum problem with free discontinuity set, Arch. Rational Mech. Anal.108 (1989), 195-218. Zbl0682.49002MR1012174
17. [17] E. Giusti, Minimal surfaces and functions with bounded variation, Birkhäuser, Boston, 1984. Zbl0545.49018MR775682
18. [18] F.H. Lin, Variational problems with free interfaces, Calc. Var.1 (1993), 149-168. Zbl0794.49038MR1261721
19. [19] J.M. Morel - S. Solimini, Variational models in image segmentation, Birkhäuser, Bostom, 1994. Zbl0827.68111
20. [20] D. Mumford - J. Shah, Optimal approximation by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math.17 (1989), 577-685. Zbl0691.49036MR997568
21. [21] L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, Canberra, 1983. Zbl0546.49019MR756417
22. [22] W.P. Ziemer, Weakly differentiable functions, Springer Verlag, Berlin, 1989. Zbl0692.46022MR1014685

1. Carlo-Romano Grisanti, On a functional depending on curvature and edges
2. Francesco Maddalena, Sergio Solimini, Regularity properties of free discontinuity sets
3. Séverine Rigot, Big pieces of $C^{1,\alpha }$-graphs for minimizers of the Mumford-Shah functional
4. Michele Carriero, Antonio Leaci, Franco Tomarelli, Strong minimizers of Blake & Zisserman functional
5. Antoine Lemenant, On the homogeneity of global minimizers for the Mumford-Shah functional when K is a smooth cone
6. F. A. Lops, F Maddalena, S Solimini, Hölder continuity conditions for the solvability of Dirichlet problems involving functionals with free discontinuities
7. Antoine Lemenant, Un théorème de régularité pour les minimiseurs de Mumford-Shah dans ${ℝ}^3$
8. Guy David, Jean-Christophe Léger, Monotonicity and separation for the Mumford–Shah problem
9. Irene Fonseca, Nicola Fusco, Regularity results for anisotropic image segmentation models
10. Francesco Maddalena, Sergio Solimini, Concentration and flatness properties of the singular set of bisected balls