no. 1
Partial regularity of free discontinuity sets, I
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 24 (1997) no. 1, pp. 1-38
followed-by Partial regularity of free discontinuity sets, II 
@article{ASNSP_1997_4_24_1_1_0,
     author = {Ambrosio, Luigi and Pallara, Diego},
     title = {Partial regularity of free discontinuity sets, {I}},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {1--38},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 24},
     number = {1},
     year = {1997},
     mrnumber = {1475771},
     language = {en},
     url = {https://www.numdam.org/item/ASNSP_1997_4_24_1_1_0/}
}
TY  - JOUR
AU  - Ambrosio, Luigi
AU  - Pallara, Diego
TI  - Partial regularity of free discontinuity sets, I
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1997
SP  - 1
EP  - 38
VL  - 24
IS  - 1
PB  - Scuola normale superiore
UR  - https://www.numdam.org/item/ASNSP_1997_4_24_1_1_0/
LA  - en
ID  - ASNSP_1997_4_24_1_1_0
ER  - 
%0 Journal Article
%A Ambrosio, Luigi
%A Pallara, Diego
%T Partial regularity of free discontinuity sets, I
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1997
%P 1-38
%V 24
%N 1
%I Scuola normale superiore
%U https://www.numdam.org/item/ASNSP_1997_4_24_1_1_0/
%G en
%F ASNSP_1997_4_24_1_1_0
Ambrosio, Luigi; Pallara, Diego. Partial regularity of free discontinuity sets, I. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 24 (1997) no. 1, pp. 1-38. https://www.numdam.org/item/ASNSP_1997_4_24_1_1_0/

[1] W.K. Allard, On the first variation of a varifold, Ann. of Math. 95 (1972), 417-491. | Zbl | MR

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

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

[4] L. Ambrosio, Variational problems in S B V, Acta App. Math. (1989), 1-40. | Zbl | MR

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

[6] L. Ambrosio - N. Fusco - D. Pallara, Partial regularity of free discontinuity sets II, (1995), to appear.

[7] A. Blake - A. Zisserman, Visual Reconstruction, M.I.T. Press, 1987. | MR

[8] A. Bonnet, On the regularity of edges in the Mumford-Shah model for image segmentation, Ann. Inst. H. Poincaré, to appear.

[9] K.A. Brakke, The motion of a surface by its mean curvature, Princeton U.P., 1978. | Zbl | MR

[10] M. Carriero - A. Leaci, Existence theorem for a Dirichlet problem withfree discontinuity set, Nonlinear Anal. 15 (1990), 661-677. | Zbl | MR

[11] M. Carriero - A. Leaci, Sk-valued maps minimizing the Lp norm of the gradient with free discontinuities, Ann. Scuola Norm. Sup. Pisa Cl. Sci IV 18 (1991), 321-352. | Zbl | MR | Numdam

[12] M. Carriero - A. Leaci - D. Pallara - E. Pascali, Euler Conditions for a Minimum Problem with Free Discontinuity Set, Preprint Dip. di Matematica 8 Lecce, 1988.

[13] 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. | Zbl | MR

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

[15] G. David - S. Semmes, On the singular set of minimizers of the Mumford - Shahfunctional, J. Math. Pures Appl., to appear. | Zbl

[16] G. David, C1 -arcs for the minimizers of the Mumford- Shah functional, SIAM J. Appl. Math. 56 (1996), 783-888. | Zbl | MR

[17] 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. | Zbl | MR

[18] E. De Giorgi - L. Ambrosio, Un nuovo tipo di funzionale del Calcolo delle Variazioni, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. (8) 82 (1988), 199-210. | Zbl | MR

[19] 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. | Zbl | MR

[20] H. Federer, Geometric measure theory, Springer Verlag, 1969. | Zbl | MR

[21] M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems, Princeton U. P., 1983. | Zbl | MR

[22] F.H. Lin, Variational problems with free interfaces, Calc. Var. 1 (1993), 149-168. | Zbl | MR

[23] J.M. Morel - S. Solimini, Variational models in image segmentation, Birkhäuser, 1994.

[24] D. Mumford - J. Shah, Optimal approximation by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math. 17 (1989) 577-685. | Zbl | MR

[25] D. Pallara, Regularity of minimizers of the Mumford-Shah functional, In: Foundations of Computational Mathematics, IMPA, Rio de Janeiro, 1997, F. Cucker and M. Shub eds, Springer, pp. 326-345. | Zbl | MR

[26] L. Simon, Lectures on Geometric Measure Theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, Canberra, 1983. | Zbl | MR