Metric space valued functions of bounded variation
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1990)
- Volume: 17, Issue: 3, page 439-478
- ISSN: 0391-173X
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topAmbrosio, Luigi. "Metric space valued functions of bounded variation." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 17.3 (1990): 439-478. <http://eudml.org/doc/84082>.
@article{Ambrosio1990,
author = {Ambrosio, Luigi},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {locally compact metric space; -convergence},
language = {eng},
number = {3},
pages = {439-478},
publisher = {Scuola normale superiore},
title = {Metric space valued functions of bounded variation},
url = {http://eudml.org/doc/84082},
volume = {17},
year = {1990},
}
TY - JOUR
AU - Ambrosio, Luigi
TI - Metric space valued functions of bounded variation
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1990
PB - Scuola normale superiore
VL - 17
IS - 3
SP - 439
EP - 478
LA - eng
KW - locally compact metric space; -convergence
UR - http://eudml.org/doc/84082
ER -
References
top- [1] E. Acerbi - N. Fusco, Semicontinuity problems in the Calculus of Variations. Arch. Rational Mech. Anal., 86, 125-145, 1986. Zbl0565.49010
- [2] L. Ambrosio, A compactness theorem for a special class of functions of bounded variation. Boll. Un. Mat. It., 3-B, 7, 857-881, 1990. Zbl0767.49001
- [3] L. Ambrosio, Existence theory for a new class of variational problems. To appear in Arch. Rational Mech. Anal. Zbl0711.49064
- [4] L. Ambrosio, Variational problems in SBV. Acta Applicandae Mathematicae, 17, 1-40, 1989. Zbl0697.49004
- [5] L. Ambrosio - G. Dal Maso, The chain rule for distributional derivative. Proc. Amer. Math. Soc., 108, 3, 691-702, 1990. Zbl0685.49027
- [6] L. Ambrosio - V.M. Tortorelli, Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence. To appear in: "Communications On Pure and Applied Mathematics". Zbl0722.49020
- [7] L. Ambrosio - S. Mortola - V.M. Tortorelli, Functionals with linear growth defined on vector valued BV functions. To appear in "Ann. Inst. H. Poincarè". Zbl0662.49007
- [8] H. Attouch, Variational convergence for functions and operators. Pitman, Boston, 1984. Zbl0561.49012
- [9] S. Baldo, Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids. To appear in: "Ann. Inst. H. Poincarè". Zbl0702.49009
- [10] A.P. Calderon - A. Zygmund, On the differentiability of functions which are of bounded variation in Tonelli's sense. Revista Union Mat. Arg., 20, 102-121, 1960. Zbl0116.31804
- [11] C. Castaing - M. Valadier, Convex analysis and measurable multifunctions. Lecture Notes in Math., 590, 1977. Zbl0346.46038
- [12] L. Cesari, Sulle funzioni a variazione limitata. Ann. Scuola Norm. Sup. Pisa, Ser. 2, Vol. 5, 1936. Zbl0014.29605JFM62.0247.03
- [13] G. Dal Maso - L. Modica, A general theory of variational functionals. "Topics in Functional Analysis 1980-81", Scuola Normale Superiore, Pisa, 1981. Zbl0493.49005
- [14] E. De Giorgi, Su una teoria generale della misura (r-1)-dimensionale in uno spazio a r dimensioni. Ann. Mat. Pura Appl., 36, 191-213, 1954. Zbl0055.28504
- [15] E. De Giorgi, Nuovi teoremi relativi alle misure (r-1)-dimensionali in uno spazio a r dimensioni. Ricerche Mat., 4, 95-113, 1955. Zbl0066.29903
- [16] E. De Giorgi - L. Ambrosio, Un nuovo tipo di funzionale del Calcolo delle Variazioni. Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Natur., 2-VIII, 82, 1989.
- [17] E. De Giorgi - M. Carriero - A. Leaci, Existence theorem for a minimum problem with free discontinuity set. Arch. Rational Mech. Anal., 108, 3, 193-218, 1989. Zbl0682.49002
- [18] E. De Giorgi - T. Franzoni, Su un tipo di convergenza variazionale. Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat. Natur., (8) 58, 842-850, 1975. Zbl0339.49005
- [19] H. Federer, Geometric Measure Theory. Springer Verlag, Berlin, 1969. Zbl0176.00801
- [20] H. Federer, A note on Gauss-Green theorem. Proc. Amer. Mat. Soc., 9, 447-451, 1958. Zbl0087.27302
- [21] H. Federer, Colloquium lectures on Geometric Measure Theory. Bull. Amer. Math. Soc., 84, 3, 291-338, 1978. Zbl0392.49021
- [22] W.H. Fleming - R. Rishel, An integral formula for total gradient variation. Arch. Math., 11, 218-222, 1960. Zbl0094.26301
- [23] E. Giusti, Minimal Surfaces and Functions of Bounded Variation. Birkäuser, Boston, 1984. Zbl0545.49018
- [24] L. Modica, The gradient theory of phase transitions and the minimal interface criterion. Arch. Rational Mech. Anal., 98, 2, 123-142, 1987. Zbl0616.76004
- [25] L. Modica - S. Mortola, Un esempio di Γ-convergenza. Boll. Un. Mat. Ital., 514-B, 285-299, 1977. Zbl0356.49008
- [26] D. Mumford - J. Shah, Boundary detection by minimizing functionals. Proc. of the IEEE conference on computer vision and pattern recognition, San Francisco, 1985.
- [27] D. Mumford - J. Shah, Optimal approximation by piecewise smooth functions and associated variational problems. Comm. on Pure and Appl. Math., 17, 4, 577-685, 1989. Zbl0691.49036
- [28] Y.G. Reshetnyak, Weak convergence of completely additive vector functions on a set. Siberian Math. J., 9, 1039-1045, 1968 (translation of Sibirsk Mat. Z., 9, 1386-1394, 1968). Zbl0169.18301
- [29] E. Stein, Singular integrals and differentiability properties of functions. Princeton University Press, 1970. Zbl0207.13501
- [30] P. Sternberg, The effect of a singular perturbation on Nonconvex Variational Problems. Arch. Rational Mech. Anal., 101, 209-260, 1988. Zbl0647.49021
- [31] A.I. Vol'pert - S.I. Huhjaev, Analysis in classes of discontinuous functions and equations of mathematical physics. Martinus Nijhoff Publisher, Dordrecht, 1985. Zbl0564.46025
- [32] A.I. Vol'pert, The spaces BV and quasilinear equations. Math. USSR. Sb., 17, 225-267, 1967. Zbl0168.07402
- [33] W.P. Ziemer, Weakly differentiable functions. Springer Verlag, Berlin, 1989. Zbl0692.46022
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