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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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1Alberti, G.. A Lusin Type Theorem for Gradients. J. Fund. Anal. 100 (1991), 110118.
2Ambrosio, L.. A Compactness Theorem for a Special Class of Functions of Bounded Variation. Boll. Un. Mat. Ital. Ser. 3B 7 (1989), 857881.
3Ambrosio, L.. Variational Problems in SBV. Ada Appl. Math. 17 (1989), 140.
4Ambrosio, L. and Dal Maso, G.. On the Relaxation in BV(Ω, Rm) of Quasiconvex Integrals J. Fund. Anal, (to appear).
5Ambrosio, L. and De Giorgi, E.. Un Nuovo tipo di Funzionale del Calcolo delle Variazioni. Atti Ace. Naz. dei Lincei, Rend. Cl. Sc. Fis. Mat. Natur. LXXXII (1988), 199210.
6Aviles, P. and Giga, Y.. Singularities and Rank One Properties of Hessian Measures. Duke Math. J. 58 (1989), 441467.
7Bouchitte, G. and Dal, G. Maso. Integral Representation and Relaxation of Convex Local Functionals on BK(Ω) preprint SISSA, April 1991).
8Castaing, C. and Valadier, M.. Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics 580 (Berlin: Springer, 1977).
9Dellacherie, C. and Meyer, P. A.. Probabilities and Potential, North Holland Mathematical Studies 29 (Paris: Hermann, 1975).
10Evans, C. and Gariepy, R. F.. Lecture Notes on Measure Theory and Fine Properties of Functions (book in preparation, we consider version 1.0).
11Fonseca, I. and M, S.ülleQuasiconvex, r. Integrands and Lower Semicontinuity in Ll. SIAM J. Anal, (to appear).
12Fonseca, I. and M, S.üller. Relaxation of Quasiconvex Functionals in BV(Ω, Rp) for Integrands f(x, u, Du) (Preprint Carnegie-Mellon Univ.).
13Gagliardo, E.. Caratterizzazione delle Traccie sulla Frontiere Relative ad alcune classi di Funzioni in piú variabili. Rend. Sent. Mat. Padova 27 (1957) 284305.
14Giusti, E.. Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics 80 (Boston: Birkhäuser, 1984).
15Rudin, W.. Real and Complex Analysis (New York: McGraw-Hill, 1966).
16Simon, L.. Lectures on Geometric Measure Theory, Proceedings of the Center for Mathematical Analysis 3 (Canberra: Australian National University, 1983).
17Ziemer, W. P.. 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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