Functionals depending on curvatures with constraints

Maria Giovanna Mora; Massimiliano Morini

Rendiconti del Seminario Matematico della Università di Padova (2000)

  • Volume: 104, page 173-199
  • ISSN: 0041-8994

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Mora, Maria Giovanna, and Morini, Massimiliano. "Functionals depending on curvatures with constraints." Rendiconti del Seminario Matematico della Università di Padova 104 (2000): 173-199. <http://eudml.org/doc/108533>.

@article{Mora2000,
author = {Mora, Maria Giovanna, Morini, Massimiliano},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {integral functional; curvature; Hausdorff measure; compactness; Hausdorff distance; semicontinuity; image segmentation},
language = {eng},
pages = {173-199},
publisher = {Seminario Matematico of the University of Padua},
title = {Functionals depending on curvatures with constraints},
url = {http://eudml.org/doc/108533},
volume = {104},
year = {2000},
}

TY - JOUR
AU - Mora, Maria Giovanna
AU - Morini, Massimiliano
TI - Functionals depending on curvatures with constraints
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2000
PB - Seminario Matematico of the University of Padua
VL - 104
SP - 173
EP - 199
LA - eng
KW - integral functional; curvature; Hausdorff measure; compactness; Hausdorff distance; semicontinuity; image segmentation
UR - http://eudml.org/doc/108533
ER -

References

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  1. [1] E. Acerbi - N. Fusco, Semicontinuity Problems in the Calculus of Variations, Arch. Rational Mech. Anal., 86 (1984), pp. 125-145. Zbl0565.49010MR751305
  2. [2] S. Agmon - A. DOUGLIS - L. NIRENBERG, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary value conditions, Comm. Pure Appl. Math., 12 (1959), pp. 623-727. Zbl0093.10401MR125307
  3. [3] G. Bellettini - G. Dal Maso - M. Paolini, Semicontinuity and Relaxation Properties of a Curvature Depending Functional in 2D, Ann. Scuola Norm. Sup. Pisa, XX (1993), pp. 247-297. Zbl0797.49013MR1233638
  4. [4] M.P. D, Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, New Jersey (1976). Zbl0326.53001MR394451
  5. [5] B.Y. Chen, Total Mean Curvature and Submanifolds of Finite Type, Series in Pure Mathematics-Volume 1, World Scientific Publishing Co Pte Ltd., Singapore (1984). Zbl0537.53049MR749575
  6. [6] G. Dal Maso: An Introduction to Γ-convergence, Birkhäuser, Boston (1993). Zbl0816.49001
  7. [7] J.M. Morel - S. Solimini, Variational Models in Image Segmentation, Birkhäuser, Boston (1995). MR1321598
  8. [8] M. Nitzberg - D. Mumford, The 2.1-D Sketch, International Conference on Computer Vision. Computer Society Press, IEEE (1990). 
  9. [9] M. Nitzberg - D. Mumford - T. Shiota, Filtering, Segmentation and Depth, Springer-Verlag, Berlin (1993). Zbl0801.68171MR1226232
  10. [10] M. Spivak, A Comprehensive Introduction to Differential Geometry, Publish or Perish, Berkeley (1979). Zbl0439.53001
  11. [11] T.J. Willmore, Note on embedded surfaces, An. Stiint. Univ. «Al. I. Cusa» Iasi Sect. I, a Mat., vol. II (1965), pp. 443-446. Zbl0171.20001MR202066
  12. [12] T.J. Willmore, Mean Curvature of Immersed Manifolds, topics in Differential Geometry, edited by H. Rund and W. F. Forbes, Academic Press, London (1976), pp. 149-156. Zbl0339.53005MR413017

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