@article{AIHPC_1996__13_4_383_0, author = {David, Guy and Semmes, Stephen}, title = {Uniform rectifiability and singular sets}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {13}, year = {1996}, pages = {383-443}, mrnumber = {1404317}, zbl = {0908.49030}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_1996__13_4_383_0} }
David, Guy; Semmes, Stephen. Uniform rectifiability and singular sets. Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) pp. 383-443. http://gdmltest.u-ga.fr/item/AIHPC_1996__13_4_383_0/
[Am] Existence theory for a new class of variational problems, Arch. Rational Mech. Anal., Vol. 111, 1990, pp. 291-322. | MR 1068374 | Zbl 0711.49064
,[CL1] Existence theorem for a Dirichlet problem with free discontinuity set, Nonlinear Analysis, Theory, Methods & Applications, Vol. 15, 1990, pp. 661-677. | Zbl 0713.49003
and ,[CL2] 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 1145314 | Zbl 0753.49018
and ,[DCL] Existence theorem for a minimum problem with free discontinuity set, Arch. Rational Mech. Anal., Vol. 108, 1989, pp. 195-218. | MR 1012174 | Zbl 0682.49002
, and ,[Da] Morceaux de graphes lipschitziens et intégrales singulières sur une surface, Revista Matematica Iberoamericana, Vol. 4, 1, 1988, pp. 73-114. | MR 1009120 | Zbl 0696.42011
,[DJ] Lipschitz approximations to hypersurfaces, harmonic measure, and singular integrals, Indiana U. Math. Journal., Vol. 39, 3, 1990, pp. 831-845. | MR 1078740 | Zbl 0758.42008
and ,[DMS] A variational method in image segmentation: Existence and approximation results, Acta Math., Vol. 168, 1992, pp. 89-151. | MR 1149865 | Zbl 0772.49006
, and ,[DS1] Singular Integrals and Rectifiable Sets in Rn: au-delà des graphes lipschitziens, Astérisque 193, Société Mathématique de France, 1991. | Zbl 0743.49018
and ,[DS2] Quantitative rectifiability and Lipschitz mappings, Transactions A.M.S., Vol. 337, 1993, pp. 855-889. | MR 1132876 | Zbl 0792.49029
and ,[DS3] Analysis of and on Uniformly Rectifiable Sets, Mathematical surveys and monographs, Vol. 38, 1993, American Mathematical Society. | MR 1251061 | Zbl 0832.42008
and ,[DS4] On the singular sets of minimizers of the Mumford-Shah functional, to appear J. Math. Pures Appl. | Zbl 0853.49010
and ,[DS5] 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 1364884 | Zbl 0887.49002
and ,[Fa] The geometry of fractal sets, Cambridge University Press, 1984. | MR 867284 | Zbl 0587.28004
,[Fe] Geometric Measure Theory, Grundlehren der Mathematishen Wissenschaften 153, Springer-Verlag 1963. | Zbl 0176.00801
,[Ga] Bounded Analytic Functions, Academic Press, 1981. | MR 628971 | Zbl 0469.30024
,[Gi] Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, 1984. | MR 775682 | Zbl 0545.49018
,[GMT] Boundaries of Prescribed Mean Curvature, Rend. Mat. Acc. Lincei s. 9, Vol. 4, 1993, pp. 197-206. | MR 1250498 | Zbl 0824.49037
, and ,[Hr]
, Ph.D. thesis, Yale university.[Je] Calderón-Zygmund Operators, Pseudodifferential Operators, and the Cauchy Integral of Calderón, Lecture Notes. in Math., Vol. 994, 1983, Springer-Verlag. | MR 706075 | Zbl 0508.42021
,[Js] Lipschitz and bi-Lipschitz functions, Rev. Mat. Iberoamericana, Vol. 4, 1988, pp. 115-122. | MR 1009121 | Zbl 0782.26007
,[Ma] Geometry of Sets and Measures in Euclidean Spaces, to appear, Cambridge Studies in Advanced Math. , Cambridge Univ. Press. | MR 1333890 | Zbl 0819.28004
,[MoS] Variational Methods in Image Segmentation, Progress in Nonlinear differential equations and their applications, Vol. 14, Birkhauser, 1995. | MR 1321598 | Zbl 0827.68111
and ,[MuS] Optimal approximations by piecewise smooth functions and associated variational problems, Comm. Pure Appl. Math., Vol. 42, 1989, pp. 577-685. | MR 997568 | Zbl 0691.49036
and ,[Se1] A criterion for the boundedness of singular integrals on hypersurfaces, Trans. Amer. Math. Soc., Vol. 311, 2, 1989, pp. 501-513. | MR 948198 | Zbl 0675.42015
,[Se2] Analysis vs. geometry on a class of rectifiable hypersurfaces in Rn, Indiana Math. J., Vol. 39, 1990, pp. 1005-1035. | MR 1087183 | Zbl 0796.42014
,[Se3] Hypersurfaces in Rn whose unit normal has small BMO norm, Proc. Amer. Math. Soc., Vol. 112, 1991, pp. 403-412. | MR 1065093 | Zbl 0733.42014
,[St] Singular integrals and differentiability properties of functions, Princeton University Press 1970. | MR 290095 | Zbl 0207.13501
,[VI] BMO functions and the ∂ equation, Pacific J. Math., Vol. 71, 1977, pp. 221-273. | MR 508035 | Zbl 0371.35035
,[V2] A remark on BMO and bounded harmonic functions, Pacific J. Math., Vol. 73, 1977, pp. 257-259. | MR 508036 | Zbl 0382.31004
,