Metric space valued functions of bounded variation
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 17 (1990) no. 3, pp. 439-478. 
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     author = {Ambrosio, Luigi},
     title = {Metric space valued functions of bounded variation},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {439--478},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 17},
     number = {3},
     year = {1990},
     mrnumber = {1079985},
     zbl = {0724.49027},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1990_4_17_3_439_0/}
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Ambrosio, Luigi. Metric space valued functions of bounded variation. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 17 (1990) no. 3, pp. 439-478. http://archive.numdam.org/item/ASNSP_1990_4_17_3_439_0/

[1] E. Acerbi - N. Fusco, Semicontinuity problems in the Calculus of Variations. Arch. Rational Mech. Anal., 86, 125-145, 1986. | Zbl

[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. | Zbl

[3] L. Ambrosio, Existence theory for a new class of variational problems. To appear in Arch. Rational Mech. Anal. | Zbl

[4] L. Ambrosio, Variational problems in SBV. Acta Applicandae Mathematicae, 17, 1-40, 1989. | Zbl

[5] L. Ambrosio - G. Dal Maso, The chain rule for distributional derivative. Proc. Amer. Math. Soc., 108, 3, 691-702, 1990. | Zbl

[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". | Zbl

[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".

[8] H. Attouch, Variational convergence for functions and operators. Pitman, Boston, 1984. | Zbl

[9] S. Baldo, Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids. To appear in: "Ann. Inst. H. Poincarè". | Numdam | Zbl

[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. | Zbl

[11] C. Castaing - M. Valadier, Convex analysis and measurable multifunctions. Lecture Notes in Math., 590, 1977. | Zbl

[12] L. Cesari, Sulle funzioni a variazione limitata. Ann. Scuola Norm. Sup. Pisa, Ser. 2, Vol. 5, 1936. | JFM | Numdam | Zbl

[13] G. Dal Maso - L. Modica, A general theory of variational functionals. "Topics in Functional Analysis 1980-81", Scuola Normale Superiore, Pisa, 1981. | Zbl

[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. | Zbl

[15] E. De Giorgi, Nuovi teoremi relativi alle misure (r-1)-dimensionali in uno spazio a r dimensioni. Ricerche Mat., 4, 95-113, 1955. | Zbl

[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. | Zbl

[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. | Zbl

[19] H. Federer, Geometric Measure Theory. Springer Verlag, Berlin, 1969. | Zbl

[20] H. Federer, A note on Gauss-Green theorem. Proc. Amer. Mat. Soc., 9, 447-451, 1958. | Zbl

[21] H. Federer, Colloquium lectures on Geometric Measure Theory. Bull. Amer. Math. Soc., 84, 3, 291-338, 1978. | Zbl

[22] W.H. Fleming - R. Rishel, An integral formula for total gradient variation. Arch. Math., 11, 218-222, 1960. | Zbl

[23] E. Giusti, Minimal Surfaces and Functions of Bounded Variation. Birkäuser, Boston, 1984. | Zbl

[24] L. Modica, The gradient theory of phase transitions and the minimal interface criterion. Arch. Rational Mech. Anal., 98, 2, 123-142, 1987. | Zbl

[25] L. Modica - S. Mortola, Un esempio di Γ-convergenza. Boll. Un. Mat. Ital., 5 14-B, 285-299, 1977. | Zbl

[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. | Zbl

[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). | Zbl

[29] E. Stein, Singular integrals and differentiability properties of functions. Princeton University Press, 1970. | Zbl

[30] P. Sternberg, The effect of a singular perturbation on Nonconvex Variational Problems. Arch. Rational Mech. Anal., 101, 209-260, 1988. | Zbl

[31] A.I. Vol'Pert - S.I. Huhjaev, Analysis in classes of discontinuous functions and equations of mathematical physics. Martinus Nijhoff Publisher, Dordrecht, 1985. | Zbl

[32] A.I. Vol'Pert, The spaces BV and quasilinear equations. Math. USSR. Sb., 17, 225-267, 1967. | Zbl

[33] W.P. Ziemer, Weakly differentiable functions. Springer Verlag, Berlin, 1989. | Zbl