The Curvature of a Set with Finite Area

Elisabetta Barozzi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1994)

  • Volume: 5, Issue: 2, page 149-159
  • ISSN: 1120-6330

Abstract

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In a paper, by myself, E. Gonzalez and I. Tamanini (see [2]), it was proven that all sets of finite perimeter do have a non trivial variational property, connected with the mean curvature of their boundaries. In the present article, that variational property is made more precise.

How to cite

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Barozzi, Elisabetta. "The Curvature of a Set with Finite Area." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 5.2 (1994): 149-159. <http://eudml.org/doc/244210>.

@article{Barozzi1994,
abstract = {In a paper, by myself, E. Gonzalez and I. Tamanini (see [2]), it was proven that all sets of finite perimeter do have a non trivial variational property, connected with the mean curvature of their boundaries. In the present article, that variational property is made more precise.},
author = {Barozzi, Elisabetta},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Calculus of variations; Geometric measure theory; Mean curvature; Boundaries of finite measure; sets of finite perimeter; mean curvature},
language = {eng},
month = {6},
number = {2},
pages = {149-159},
publisher = {Accademia Nazionale dei Lincei},
title = {The Curvature of a Set with Finite Area},
url = {http://eudml.org/doc/244210},
volume = {5},
year = {1994},
}

TY - JOUR
AU - Barozzi, Elisabetta
TI - The Curvature of a Set with Finite Area
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1994/6//
PB - Accademia Nazionale dei Lincei
VL - 5
IS - 2
SP - 149
EP - 159
AB - In a paper, by myself, E. Gonzalez and I. Tamanini (see [2]), it was proven that all sets of finite perimeter do have a non trivial variational property, connected with the mean curvature of their boundaries. In the present article, that variational property is made more precise.
LA - eng
KW - Calculus of variations; Geometric measure theory; Mean curvature; Boundaries of finite measure; sets of finite perimeter; mean curvature
UR - http://eudml.org/doc/244210
ER -

References

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  1. ADAMS, R. A., Sobolev Spaces. Academic Press, New York-London-Toronto-Sydney-San Francisco1984. Zbl0314.46030MR450957
  2. BAROZZI, E. - GONZALEZ, E. - TAMANINI, I., The Mean Curvature of a Set of Finite Perimeter. Proc. A.M.S., 99, 1987, 313-316. MR870791DOI10.2307/2046631
  3. GIUSTI, E., Minimal Surfaces and Functions of Bounded Variation. Birkhäuser, Boston-Basel-Stuttgart1984. Zbl0545.49018MR775682
  4. GONZALEZ, E. H. A. - MASSARI, U., Variational mean curvature. Rend. Sem. Mat. Univer. Politecnic. Torino, to appear. Zbl0819.49025MR1289900
  5. GONZALES, E. H. A. - MASSARI, U. - TAMANINI, I., Boundaries of prescribed mean curvature. Rend. Mat. Acc. Lincei, s. 9, v. 4, 1993, 197-206. Zbl0824.49037MR1250498
  6. MASSARI, U., Esistenza e regolarità delle ipersuperfici di curvatura media assegnata in R n . Arch. Rat. Mech. An., 55, 1974, 357-382. Zbl0305.49047MR355766
  7. MASSARI, U., Frontiere orientate di curvatura media assegnata in L p . Rend. Sem. Mat. Univ. Padova, 53, 1975, 37-52. Zbl0358.49019MR417905
  8. MASSARI, U. - MIRANDA, M., Minimal Surfaces of Codimension One. North-Holland, Amsterdam1984. Zbl0565.49030MR795963

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