Uniform rectifiability and singular sets
Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) no. 4, pp. 383-443.
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     author = {David, Guy and Semmes, Stephen},
     title = {Uniform rectifiability and singular sets},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {383--443},
     publisher = {Gauthier-Villars},
     volume = {13},
     number = {4},
     year = {1996},
     mrnumber = {1404317},
     zbl = {0908.49030},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1996__13_4_383_0/}
}
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David, Guy; Semmes, Stephen. Uniform rectifiability and singular sets. Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) no. 4, pp. 383-443. http://archive.numdam.org/item/AIHPC_1996__13_4_383_0/

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

[CL1] M. Carriero and A. Leaci, Existence theorem for a Dirichlet problem with free discontinuity set, Nonlinear Analysis, Theory, Methods & Applications, Vol. 15, 1990, pp. 661-677. | Zbl

[CL2] M. Carriero and A. Leaci, Sk-Valued Maps minimizing the Lp norm of the gradient with free discontinuities, Ann. Sc. Norm. Sup. Pisa, Vol. 18, 1991, pp. 321-352. | Numdam | MR | Zbl

[DCL] E. De Giorgi, M. Carriero and A. Leaci, Existence theorem for a minimum problem with free discontinuity set, Arch. Rational Mech. Anal., Vol. 108, 1989, pp. 195-218. | MR | Zbl

[Da] G. David, Morceaux de graphes lipschitziens et intégrales singulières sur une surface, Revista Matematica Iberoamericana, Vol. 4, 1, 1988, pp. 73-114. | MR | Zbl

[DJ] G. David and D. Jerison, Lipschitz approximations to hypersurfaces, harmonic measure, and singular integrals, Indiana U. Math. Journal., Vol. 39, 3, 1990, pp. 831-845. | MR | Zbl

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

[DS1] G. David and S. Semmes, Singular Integrals and Rectifiable Sets in Rn: au-delà des graphes lipschitziens, Astérisque 193, Société Mathématique de France, 1991. | Numdam | Zbl

[DS2] G. David and S. Semmes, Quantitative rectifiability and Lipschitz mappings, Transactions A.M.S., Vol. 337, 1993, pp. 855-889. | MR | Zbl

[DS3] G. David and S. Semmes, Analysis of and on Uniformly Rectifiable Sets, Mathematical surveys and monographs, Vol. 38, 1993, American Mathematical Society. | MR | Zbl

[DS4] G. David and S. Semmes, On the singular sets of minimizers of the Mumford-Shah functional, to appear J. Math. Pures Appl. | Zbl

[DS5] G. David and S. Semmes, On a variational problem from image processing, Proceedings of the conference in Honor of Jean-Pierre Kahane, Journ. of Fourier Analysis and Applications, 1995, pp. 161-187. | MR | Zbl

[Fa] K. Falconer, The geometry of fractal sets, Cambridge University Press, 1984. | MR | Zbl

[Fe] H. Federer, Geometric Measure Theory, Grundlehren der Mathematishen Wissenschaften 153, Springer-Verlag 1963. | Zbl

[Ga] J. Garnett, Bounded Analytic Functions, Academic Press, 1981. | MR | Zbl

[Gi] E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, 1984. | MR | Zbl

[GMT] H. Gonzales, U. Massari and I. Tamanini, Boundaries of Prescribed Mean Curvature, Rend. Mat. Acc. Lincei s. 9, Vol. 4, 1993, pp. 197-206. | MR | Zbl

[Hr] T. Hrycak, Ph.D. thesis, Yale university.

[Je] J.L. Journé, Calderón-Zygmund Operators, Pseudodifferential Operators, and the Cauchy Integral of Calderón, Lecture Notes. in Math., Vol. 994, 1983, Springer-Verlag. | MR | Zbl

[Js] P. Jones, Lipschitz and bi-Lipschitz functions, Rev. Mat. Iberoamericana, Vol. 4, 1988, pp. 115-122. | MR | Zbl

[Ma] P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, to appear, Cambridge Studies in Advanced Math. , Cambridge Univ. Press. | MR | Zbl

[MoS] J.-M. Morel and S. Solimini, Variational Methods in Image Segmentation, Progress in Nonlinear differential equations and their applications, Vol. 14, Birkhauser, 1995. | MR | Zbl

[MuS] D. Mumford and J. Shah, Optimal approximations by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math., Vol. 42, 1989, pp. 577-685. | MR | Zbl

[Se1] S. Semmes, A criterion for the boundedness of singular integrals on hypersurfaces, Trans. Amer. Math. Soc., Vol. 311, 2, 1989, pp. 501-513. | MR | Zbl

[Se2] S. Semmes, Analysis vs. geometry on a class of rectifiable hypersurfaces in Rn, Indiana Math. J., Vol. 39, 1990, pp. 1005-1035. | MR | Zbl

[Se3] S. Semmes, Hypersurfaces in Rn whose unit normal has small BMO norm, Proc. Amer. Math. Soc., Vol. 112, 1991, pp. 403-412. | MR | Zbl

[St] E.M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press 1970. | MR | Zbl

[VI] N. Varopoulos, BMO functions and the ∂ equation, Pacific J. Math., Vol. 71, 1977, pp. 221-273. | MR | Zbl

[V2] N. Varopoulos, A remark on BMO and bounded harmonic functions, Pacific J. Math., Vol. 73, 1977, pp. 257-259. | MR | Zbl