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Rank one property for derivatives of functions with bounded variation

  • Giovanni Alberti (a1)

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

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

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

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

17 W. 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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