Lops, F. A.; Maddalena, F; Solimini, S
Hölder continuity conditions for the solvability of Dirichlet problems involving functionals with free discontinuities
Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 6 , p. 639-673
Zbl 1001.49018 | MR 1862638 | 1 citation dans Numdam
URL stable : http://www.numdam.org/item?id=AIHPC_2001__18_6_639_0

Bibliographie

[1] Ambrosio L., Compactness theorem for a special class of functions of bounded variation, Boll. Un. Mat. Ital. 3-B (1989) 857-881. MR 1032614 | Zbl 0767.49001

[2] Ambrosio L., Existence theory for a new class of variational problems, Arch. Rat. Mech. Anal. 111 (1990) 291-322. MR 1068374 | Zbl 0711.49064

[3] Ambrosio L., A new proof of the SBV compactness theorem, Calc. Var. 3 (1995) 127-137. MR 1384840 | Zbl 0837.49011

[4] Ambrosio L., Fusco N., Pallara D., Partial regularity of free discontinuity sets, II, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 24 (4) (1997) 39-62. Numdam | MR 1475772 | Zbl 0896.49024

[5] Carriero M., Leaci A., Existence theorem for a Dirichlet problem with free discontinuity set, Nonlinear Anal. 15 (1990) 661-667. MR 1073957 | Zbl 0713.49003

[6] Dal Maso G., Morel J.M., Solimini S., Une approche variationelle en traitement d'images: résultats d'existence et d'approximation, C. Rend. Acad. Sc. Paris, Série I 308 (1989) 549-554. MR 999453 | Zbl 0682.49003

[7] Dal Maso G., Morel J.M., Solimini S., A variational method in image segmentation: existence and approximation results, Acta Mat. 168 (1992) 89-151. MR 1149865 | Zbl 0772.49006

[8] David G., Semmes S., On the singular set of minimizers of Mumford-Shah functional, J. Math. Pures Appl. 803 (1989) 549-554.

[9] David G., Semmes S., Uniform rectifiability and singular set, Annales de l'I.H.P. 13 (4) (1996) 383-443. Numdam | MR 1404317 | Zbl 0908.49030

[10] De Giorgi E., Ambrosio L., Un nuovo tipo di funzionale del calcolo delle variazioni, Atti Acad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. s. 8 82 (1988) 199-210. MR 1152641 | Zbl 0715.49014

[11] De Giorgi E., Carriero M., Leaci A., Existence theorem for a minimum problem with free discontinuity set, Arch. Rat. Mech. Anal. 108 (1989) 195-218. MR 1012174 | Zbl 0682.49002

[12] Dibos F., Uniform rectifiability of image segmentation obtained by variational methods, J. Math. Pures Appl. 803 (1989) 549-554.

[13] Dibos F., Koepfler G., Propriété de régularité des contours d'une image segmentée, C. Rend. Acad. Sc. Paris, Série I 313 (1991) 573-578. MR 1133487 | Zbl 0779.49004

[14] Federer H., Geometric Measure Theory, Springer, Boston, 1969. MR 257325 | Zbl 0874.49001

[15] Kinderlehrer D., Stampacchia G., Variational Inequalities and Applications, Academic Press, Boston, 1980. MR 567696

[16] Maddalena F., Solimini S., Concentration and flatness properties of the singular set of bisected balls, Ann. Scuola Norm. Sup. Pisa (to appear). Numdam | MR 1896080 | Zbl 02216901

[17] Maddalena F., Solimini S., Lower semicontinuity properties for functionals with free discontinuities (to appear). MR 1860049 | Zbl 1013.49010

[18] Morel J.M., Solimini S., Variational Methods in Image Segmentation, Birkhäuser, Boston, 1994. MR 1321598

[19] Morrey C.B., Multiple integrals in the calculus of variations, Springer, Heidelberg, 1966. MR 202511 | Zbl 0142.38701

[20] Mumford D., Shah S., Optimal approximation by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math. XLII-4 (1989). MR 997568 | Zbl 0691.49036

[21] Solimini S., Simplified excision techniques for Free Discontinuity Problems in several variables, J. Funct. Anal. 151 (1) (1997) 1-34. MR 1487768 | Zbl 0891.49007