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.
In questa nota presentiamo brevemente alcuni nostri recenti risultati ([1def]) relativi alla definizione di integrale non-lineare alla Weierstrass su varietà BV, possibilmente discontinue e non di Sobolev.
@article{RLINA_1989_8_83_1_101_0,
author = {Primo Brandi and Anna Salvadori},
title = {On a class of variational integrals over BV varieties},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
volume = {83},
year = {1989},
pages = {101-108},
zbl = {0735.49040},
mrnumber = {1142446},
language = {en},
url = {http://dml.mathdoc.fr/item/RLINA_1989_8_83_1_101_0}
}
Brandi, Primo; 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, Tome 83 (1989) pp. 101-108. http://gdmltest.u-ga.fr/item/RLINA_1989_8_83_1_101_0/
[1] and , (a) 1978. Sull'integrale debole alla Burkill-Cesari. Atti Sem. Mat. Univ. Modena, 27: 12-38. | MR 551085 | Zbl 0429.28008
and , (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. | MR 881421 | Zbl 0613.49030
and , (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.
and , (d) A quasi-additivity type condition and the integral over a BV variety. Pacific J., to appear. | MR 1073517 | Zbl 0759.49010
and , (e) 1989. On the non-parametric integral over a BV surface. J. Nonlinear Anal., 13: 1127-1137. | MR 1020721 | Zbl 0694.49029
and , (f) 1989. On the lower semicontinuity of certain integrals of the Calculus of Variations. J. Math. Anal. Appl., 144: 183-205. | MR 1022570 | Zbl 0706.49011
[2] , 1971. Burkill-Cesari integrals of quasi additive interval functions. Pacific. J., 37: 635- 654. | MR 313482 | Zbl 0226.28011
[3] , (a) 1962. Quasi additive set functions and the concept of integral over a variety. Trans. Amer. Math. Soc., 102: 94-113. | MR 142723 | Zbl 0115.26902
, (b) 1962. Extension problem for quasi additive set functions and Radon-Nikodym derivatives. Trans. Amer. Math. Soc., 102: 114-146. | MR 142724 | Zbl 0115.27001
[4] , and , (a) 1988. Discontinuous solutions in problems of optimization. Annali Scuola Normale Sup. Pisa, 15: 219-237. | MR 1007398 | Zbl 0673.49020
, and , (b) 1987. Existence theorems concerning simple integrals of the calculus of variations for discontinuous solutions. Archive Rat. Mech. Anal., 98: 307-328. | MR 872750 | Zbl 0618.49004
, and , (c) 1988. Existence theorems for multiple integrals of the calculus of variations for discontinuous solutions. Annali Mat. Pura Appl., 52: 95-121. | MR 980974 | Zbl 0668.49018
[5] , 1961. On the definition and properties of certain variational integrals. Trans. Amer Math Soc., 101: 139-167. | MR 138018 | Zbl 0102.04601
[6] , 1983. Nonlinear integration and Weierstrass integral over a manifold, connection with theorems on martingales. J.O.T.A., 41: 213-237. | MR 718046 | Zbl 0497.49035
[7] , (a) 1968. The Burkill-Cesari integral. Duke Math. J., 35: 61-78. | MR 219690 | Zbl 0165.06702
, (b) 1968. The generalized Weierstrass-type integral . Ann. Scuola Norm. Sup. Pisa, 22: 163-192. | MR 248317 | Zbl 0174.09203