no. 6
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, pp. 639-673. 
@article{AIHPC_2001__18_6_639_0,
     author = {Lops, F. A. and Maddalena, F and Solimini, S},
     title = {H\"older continuity conditions for the solvability of {Dirichlet} problems involving functionals with free discontinuities},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {639--673},
     publisher = {Elsevier},
     volume = {18},
     number = {6},
     year = {2001},
     mrnumber = {1862638},
     zbl = {1001.49018},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2001__18_6_639_0/}
}
TY  - JOUR
AU  - Lops, F. A.
AU  - Maddalena, F
AU  - Solimini, S
TI  - Hölder continuity conditions for the solvability of Dirichlet problems involving functionals with free discontinuities
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2001
SP  - 639
EP  - 673
VL  - 18
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/item/AIHPC_2001__18_6_639_0/
LA  - en
ID  - AIHPC_2001__18_6_639_0
ER  - 
%0 Journal Article
%A Lops, F. A.
%A Maddalena, F
%A Solimini, S
%T Hölder continuity conditions for the solvability of Dirichlet problems involving functionals with free discontinuities
%J Annales de l'I.H.P. Analyse non linéaire
%D 2001
%P 639-673
%V 18
%N 6
%I Elsevier
%U http://www.numdam.org/item/AIHPC_2001__18_6_639_0/
%G en
%F AIHPC_2001__18_6_639_0
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, pp. 639-673. http://www.numdam.org/item/AIHPC_2001__18_6_639_0/

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

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

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

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

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

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

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

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

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