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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 123, Issue 2
  • January 1993, pp. 239-274

Rank one property for derivatives of functions with bounded variation

  • Giovanni Alberti (a1)
  • DOI: http://dx.doi.org/10.1017/S030821050002566X
  • Published online: 14 November 2011
Abstract
Synopsis

In this paper we introduce a new tool in geometric measure theory and then we apply it to study the rank properties of the derivatives of vector functions with bounded variation.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1G. Alberti . A Lusin Type Theorem for Gradients. J. Fund. Anal. 100 (1991), 110118.

6P. Aviles and Y. Giga . Singularities and Rank One Properties of Hessian Measures. Duke Math. J. 58 (1989), 441467.

8C. Castaing and M. Valadier . Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580 (Berlin: Springer, 1977).

14E. Giusti . Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics 80 (Boston: Birkhäuser, 1984).

17W. P. Ziemer . Weakly Differentiable Functions, Sobolev Spaces and Functions of Bounded Variation (Berlin: Springer, 1989).

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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