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Volumn 13, Issue 4, 1996, Pages 383-443

Uniform rectifiability and singular sets

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONAL MINIMIZATION; INEQUALITY; RECTIFIABILITY;

EID: 0030372923     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(16)30109-3     Document Type: Article
Times cited : (16)

References (29)
  • 1
    • 0000465804 scopus 로고
    • Existence theory for a new class of variational problems
    • L. Ambrosio Existence theory for a new class of variational problems Arch. Rational Mech. Anal. Vol. 111 1990 291 322
    • (1990) Arch. Rational Mech. Anal. , vol.Vol. 111 , pp. 291-322
    • Ambrosio, L.1
  • 3
    • 0012944927 scopus 로고
    • Sk-Valued Maps minimizing the Lp norm of the gradient with free discontinuities
    • p norm of the gradient with free discontinuities Ann. Sc. Norm. Sup. Pisa Vol. 18 1991 321 352
    • (1991) Ann. Sc. Norm. Sup. Pisa , vol.Vol. 18 , pp. 321-352
    • Carriero, M.1    Leaci, A.2
  • 4
    • 0000532812 scopus 로고
    • Existence theorem for a minimum problem with free discontinuity set
    • E. De Giorgi M. Carriero A. Leaci Existence theorem for a minimum problem with free discontinuity set Arch. Rational Mech. Anal. Vol. 108 1989 195 218
    • (1989) Arch. Rational Mech. Anal. , vol.Vol. 108 , pp. 195-218
    • De Giorgi, E.1    Carriero, M.2    Leaci, A.3
  • 5
    • 0009412910 scopus 로고
    • Lipschitz approximations to hypersurfaces, harmonic measure, and singular integrals
    • G. David D. Jerison Lipschitz approximations to hypersurfaces, harmonic measure, and singular integrals Indiana U. Math. Journal. Vol. 39 3 1990 831 845
    • (1990) Indiana U. Math. Journal. , vol.Vol. 39 , Issue.3 , pp. 831-845
    • David, G.1    Jerison, D.2
  • 6
    • 0002874591 scopus 로고
    • A variational method in image segmentation: Existence and approximation results
    • G. Dal Maso J.-M. Morel S. Solimini A variational method in image segmentation: Existence and approximation results Acta Math. Vol. 168 1992 89 151
    • (1992) Acta Math. , vol.Vol. 168 , pp. 89-151
    • Dal Maso, G.1    Morel, J.-M.2    Solimini, S.3
  • 7
    • 85119468092 scopus 로고    scopus 로고
    • n : au-delà des graphes lipschitziens, Astérisque 193 , Société Mathématique de France, 1991.
  • 8
    • 84968497861 scopus 로고
    • Quantitative rectifiability and Lipschitz mappings
    • G. David S. Semmes Quantitative rectifiability and Lipschitz mappings Transactions A.M.S. Vol. 337 1993 855 889
    • (1993) Transactions A.M.S. , vol.Vol. 337 , pp. 855-889
    • David, G.1    Semmes, S.2
  • 9
    • 0003748461 scopus 로고
    • Analysis of and on Uniformly Rectifiable Sets
    • G. David S. Semmes Analysis of and on Uniformly Rectifiable Sets Mathematical surveys and monographs Vol. 38 1993 American Mathematical Society
    • (1993)
    • David, G.1    Semmes, S.2
  • 10
    • 85119469258 scopus 로고    scopus 로고
    • G. David and S. Semmes, On the singular sets of minimizers of the Mumford-Shah functional, to appear J. Math. Pures Appl .
  • 11
    • 85119465679 scopus 로고    scopus 로고
    • 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.
  • 12
    • 0003418232 scopus 로고
    • Geometric Measure Theory
    • H. Federer Geometric Measure Theory Grundlehren der Mathematishen Wissenschaften 153 1963 Springer-Verlag
    • (1963)
    • Federer, H.1
  • 13
    • 0003604854 scopus 로고
    • Bounded Analytic Functions
    • J. Garnett Bounded Analytic Functions 1981 Academic Press
    • (1981)
    • Garnett, J.1
  • 14
    • 0004193690 scopus 로고
    • Minimal Surfaces and Functions of Bounded Variation
    • E. Giusti Minimal Surfaces and Functions of Bounded Variation 1984 Birkhäuser
    • (1984)
    • Giusti, E.1
  • 16
    • 85119465918 scopus 로고    scopus 로고
    • T. Hrycak, Ph.D. thesis , Yale university.
  • 17
    • 0038563974 scopus 로고
    • Lipschitz and bi-Lipschitz functions
    • P. Jones Lipschitz and bi-Lipschitz functions Rev. Mat. Iberoamericana Vol. 4 1988 115 122
    • (1988) Rev. Mat. Iberoamericana , vol.Vol. 4 , pp. 115-122
    • Jones, P.1
  • 18
    • 0003639953 scopus 로고
    • Variational Methods in Image Segmentation
    • J.-M. Morel S. Solimini Variational Methods in Image Segmentation Progress in Nonlinear differential equations and their applications Vol. 14 1995 Birkhauser
    • (1995)
    • Morel, J.-M.1    Solimini, S.2
  • 19
    • 84990602490 scopus 로고
    • Optimal approximations by piecewise smooth functions and associated variational problems
    • D. Mumford J. Shah Optimal approximations by piecewise smooth functions and associated variational problems Comm. Pure Appl. Math. Vol. 42 1989 577 685
    • (1989) Comm. Pure Appl. Math. , vol.Vol. 42 , pp. 577-685
    • Mumford, D.1    Shah, J.2
  • 20
    • 0012054931 scopus 로고
    • A criterion for the boundedness of singular integrals on hypersurfaces
    • S. Semmes A criterion for the boundedness of singular integrals on hypersurfaces Trans. Amer. Math. Soc. Vol. 311 2 1989 501 513
    • (1989) Trans. Amer. Math. Soc. , vol.Vol. 311 , Issue.2 , pp. 501-513
    • Semmes, S.1
  • 21
    • 0000750069 scopus 로고
    • Analysis vs. geometry on a class of rectifiable hypersurfaces in Rn
    • n Indiana Math. J. Vol. 39 1990 1005 1035
    • (1990) Indiana Math. J. , vol.Vol. 39 , pp. 1005-1035
    • Semmes, S.1
  • 22
    • 84968497872 scopus 로고
    • Hypersurfaces in Rn whose unit normal has small BMO norm
    • n whose unit normal has small BMO norm Proc. Amer. Math. Soc. Vol. 112 1991 403 412
    • (1991) Proc. Amer. Math. Soc. , vol.Vol. 112 , pp. 403-412
    • Semmes, S.1
  • 23
    • 0003799686 scopus 로고
    • Singular integrals and differentiability properties of functions
    • E.M. Stein Singular integrals and differentiability properties of functions 1970 Princeton University Press
    • (1970)
    • Stein, E.M.1
  • 25
    • 0039873851 scopus 로고
    • A remark on BMO and bounded harmonic functions
    • N. Varopoulos A remark on BMO and bounded harmonic functions Pacific J. Math. Vol. 73 1977 257 259
    • (1977) Pacific J. Math. , vol.Vol. 73 , pp. 257-259
    • Varopoulos, N.1
  • 26
    • 0003104844 scopus 로고
    • Morceaux de graphes lipschitziens et intégrales singulières sur une surface
    • G. David Morceaux de graphes lipschitziens et intégrales singulières sur une surface Revista Matematica Iberoamericana Vol. 4 1 1988 73 114
    • (1988) Revista Matematica Iberoamericana , vol.Vol. 4 , Issue.1 , pp. 73-114
    • David, G.1
  • 27
    • 0003986822 scopus 로고
    • The geometry of fractal sets
    • K. Falconer The geometry of fractal sets 1984 Cambridge University Press
    • (1984)
    • Falconer, K.1
  • 28
    • 1842780738 scopus 로고
    • Calderón-Zygmund Operators, Pseudodifferential Operators, and the Cauchy Integral of Calderón
    • J.L. Journé Calderón-Zygmund Operators, Pseudodifferential Operators, and the Cauchy Integral of Calderón Lecture Notes, in Math. Vol. 994 1983 Springer-Verlag
    • (1983)
    • Journé, J.L.1
  • 29
    • 85119464878 scopus 로고    scopus 로고
    • P. Mattila, Geometry of Sets and Measures in Euclidean Spaces, to appear, Cambridge Studies in Advanced Math ., Cambridge Univ. Press.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.