On a class of variational integrals over BV varieties

Primo Brandi; Anna Salvadori

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1989)

  • Volume: 83, Issue: 1, page 101-108
  • ISSN: 1120-6330

Abstract

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We present here our most recent results ([1def]) about the definition of non-linear Weiertrass-type integrals over BV varieties, possibly discontinuous and not necessarily Sobolev's.

How to cite

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Brandi, Primo, and Salvadori, Anna. "On a class of variational integrals over BV varieties." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 83.1 (1989): 101-108. <http://eudml.org/doc/287237>.

@article{Brandi1989,
abstract = {We present here our most recent results ([1def]) about the definition of non-linear Weiertrass-type integrals over BV varieties, possibly discontinuous and not necessarily Sobolev's.},
author = {Brandi, Primo, Salvadori, Anna},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Calculus of variations on BV varieties; Weierstrass integrals; Burkill-Cesari integrals; non-linear Weierstrass-type integrals; BV varieties},
language = {eng},
month = {12},
number = {1},
pages = {101-108},
publisher = {Accademia Nazionale dei Lincei},
title = {On a class of variational integrals over BV varieties},
url = {http://eudml.org/doc/287237},
volume = {83},
year = {1989},
}

TY - JOUR
AU - Brandi, Primo
AU - Salvadori, Anna
TI - On a class of variational integrals over BV varieties
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1989/12//
PB - Accademia Nazionale dei Lincei
VL - 83
IS - 1
SP - 101
EP - 108
AB - We present here our most recent results ([1def]) about the definition of non-linear Weiertrass-type integrals over BV varieties, possibly discontinuous and not necessarily Sobolev's.
LA - eng
KW - Calculus of variations on BV varieties; Weierstrass integrals; Burkill-Cesari integrals; non-linear Weierstrass-type integrals; BV varieties
UR - http://eudml.org/doc/287237
ER -

References

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  1. BRANDI, P. and SALVADORI, A., (a) 1978. Sull'integrale debole alla Burkill-Cesari. Atti Sem. Mat. Univ. Modena, 27: 12-38. Zbl0429.28008MR551085
  2. BRANDI, P. and SALVADORI, A., (b) 1984. Existence, semicontinuity and representation for the integrals of the Calculus of Variations. The BV case. Atti Convegno celebrativo I centenario Circolo Matematico di Palermo: 447-462. Zbl0613.49030MR881421
  3. BRANDI, P. and SALVADORI, A., (c) 1987. L'integrale del Calcolo delle Variazioni alla Weierstrass lungo curve BV e confronto con i funzionali integrali di Lebesgue e Serrin. Atti Sem. Mat. Univ. Modena, 35. MR937972
  4. BRANDI, P. and SALVADORI, A., (d) A quasi-additivity type condition and the integral over a BV variety. Pacific J., to appear. Zbl0759.49010
  5. BRANDI, P. and SALVADORI, A., (e) 1989. On the non-parametric integral over a BV surface. J. Nonlinear Anal., 13: 1127-1137. Zbl0694.49029MR1020721DOI10.1016/0362-546X(89)90001-1
  6. BRANDI, P. and SALVADORI, A., (f) 1989. On the lower semicontinuity of certain integrals of the Calculus of Variations. J. Math. Anal. Appl., 144: 183-205. Zbl0706.49011MR1022570DOI10.1016/0022-247X(89)90368-5
  7. BRECKENRIDGE, J.C., 1971. Burkill-Cesari integrals of quasi additive interval functions. Pacific. J., 37: 635- 654. Zbl0226.28011MR313482
  8. CESARI, L., (a) 1962. Quasi additive set functions and the concept of integral over a variety. Trans. Amer. Math. Soc., 102: 94-113. Zbl0115.26902MR142723
  9. CESARI, L., (b) 1962. Extension problem for quasi additive set functions and Radon-Nikodym derivatives. Trans. Amer. Math. Soc., 102: 114-146. Zbl0115.27001MR142724
  10. CESARI, L., BRANDI, P. and SALVADORI, A., (a) 1988. Discontinuous solutions in problems of optimization. Annali Scuola Normale Sup. Pisa, 15: 219-237. Zbl0673.49020MR1007398
  11. CESARI, L., BRANDI, P. and SALVADORI, A., (b) 1987. Existence theorems concerning simple integrals of the calculus of variations for discontinuous solutions. Archive Rat. Mech. Anal., 98: 307-328. Zbl0618.49004MR872750DOI10.1007/BF00276912
  12. CESARI, L., BRANDI, P. and SALVADORI, A., (c) 1988. Existence theorems for multiple integrals of the calculus of variations for discontinuous solutions. Annali Mat. Pura Appl., 52: 95-121. Zbl0668.49018MR980974DOI10.1007/BF01766143
  13. SERRIN, J., 1961. On the definition and properties of certain variational integrals. Trans. Amer Math Soc., 101: 139-167. Zbl0102.04601MR138018
  14. VINTI, C., 1983. Nonlinear integration and Weierstrass integral over a manifold, connection with theorems on martingales. J.O.T.A., 41: 213-237. Zbl0497.49035MR718046DOI10.1007/BF00934444
  15. WARNER, G., (a) 1968. The Burkill-Cesari integral. Duke Math. J., 35: 61-78. Zbl0165.06702MR219690
  16. WARNER, G., (b) 1968. The generalized Weierstrass-type integral ∫ f ⁢ ( ξ , ϕ ) . Ann. Scuola Norm. Sup. Pisa, 22: 163-192. Zbl0174.09203MR248317

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