@article{AIHPC_1994__11_1_91_0, author = {Amar, Micol and Bellettini, Giovanni}, title = {A notion of total variation depending on a metric with discontinuous coefficients}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {11}, year = {1994}, pages = {91-133}, mrnumber = {1259102}, zbl = {0842.49016}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_1994__11_1_91_0} }
Amar, M.; Bellettini, G. A notion of total variation depending on a metric with discontinuous coefficients. Annales de l'I.H.P. Analyse non linéaire, Tome 11 (1994) pp. 91-133. http://gdmltest.u-ga.fr/item/AIHPC_1994__11_1_91_0/
[1] A lusin Type Theorem for Gradients, J. Funct. Anal., Vol. 100 (1), 1991, pp. 110-118. | MR 1124295 | Zbl 0752.46025
,[2] Traces of Bounded Vectorfields and the Divergence Theorm, preprint Univ. Trento, 1983. | MR 750538
,[3] Pairings Between Measures and Bounded Functions and Compensated Compactness, Ann. Mat. Pura e Appl., (4), Vol. 135, 1983, pp. 293-318. | MR 750538 | Zbl 0572.46023
,[4] Anisotropic Singular Perturbations. The Vectorial Case, Research Report n. 92-NA-015, Carnegie Mellon University, 1992.
and ,[5] Integral Representation of Convex Functionals on a Space of Measures, J. Funct. Anal., Vol. 80, 1988, pp. 398-420. | MR 961907 | Zbl 0662.46009
and ,[6] Singular Perturbations of Variational Problems Arising from a Two-Phase Transition Model, Appl. Math. and Opt., Vol. 21, 1990, pp. 289-315. | MR 1036589 | Zbl 0695.49003
,[7] MASO, Integral Representation and Relaxation of Convex Local Functionals on BV(Ω), preprint SISSA, April 1991, to appear on Ann. Scuola Norm. Sup., Pisa. | Numdam | MR 1267597
and[8] Analyse Fonctionnelle. Théorie et Applications, Masson, Paris, 1983. | MR 697382 | Zbl 0511.46001
,[9] On the Foundations of Calculus of Variations, Trans. Amer. Math., Soc., Vol. 49, 1941, pp. 173-198. | MR 3475 | Zbl 0024.41703
and ,[10] Metric Methods in Finsler Spaces and in the Foundations of Geometry, Ann. of Math. Studies, Vol. 8, Princeton Univ. Press, Princeton, 1942. | MR 7251 | Zbl 0063.00672
,[11] Semicontinuity, Relaxation and Integral Representation in the Calculus of Variations, Longman, Harlow, 1989. | MR 1020296 | Zbl 0669.49005
,[12] Integral Representation and Relaxation of Local Functionals, Nonlinear Analysis, Theory, Methods & Applications, Vol. 9, 1985, pp. 515-532. | Zbl 0527.49008
and ,[13] Convex Analysis and Measurable Multifunctions, Lect. Not. in Math., Vol. 580, Springer-Verlag, Berlin, 1977. | MR 467310 | Zbl 0346.46038
and ,[14] Direct Methods in the Calculus of Variations, Springer-Verlag, Berlin, 1989. | MR 990890 | Zbl 0703.49001
,[15] Integral Representation on BV(Ω) of Γ-Limits of Variational Integrals, Manuscripta Math., Vol. 30, 1980, pp. 387-416. | MR 567216 | Zbl 0435.49016
,[16] An Introduction to Γ-Convergence, preprint SISSA, 1992, Trieste, to appear on Birkhäuser. | MR 1201152 | Zbl 0816.49001
,[17] A General Theory of Variational Functionals, in: Topics in Functional Analysis (1980-1981), Quaderni Scuola Norm. Sup. Pisa, Pisa, 1980, pp. 149-221. | MR 671757 | Zbl 0493.49005
and ,[18] Geometria sulle Varietá di Lipschitz, preprint Univ. di Roma "La Sapienza", 1992, pp. 1-38.
,[19] Distanza Intriseca su una Varietà Riemanniana di Lipschitz, Rend. Sem. Mat. Univ. Pol. Torino, Vol. 46, 1988, pp. 157-170. | MR 1084564 | Zbl 0719.53047
and ,[20] Lenght of Curves on Lip manifolds, Rend. Mat. Acc. Lincei, Vol. 1, (9), 1990, pp. 215-221. | MR 1083250 | Zbl 0719.53046
and ,[21] Integral Distance on a Lipschitz Riemannian Manifold, Math. Zeitschrift, Vol. 207, 1991, pp. 223-243. | MR 1109664 | Zbl 0722.58006
and ,[22] Nuovi Teoremi Relativi alle Misure (r-1)-dimensionali in uno Spazio a r Dimensioni, Ricerche Mat. IV, 1955, pp. 95-113. | MR 74499 | Zbl 0066.29903
,[23] Conversazioni di Matematica, Quaderni Dip. Mat. Univ. Lecce, 1988- 1990, Vol. 2, 1990.
,[24] Su Alcuni Problemi Comuni all'Analisi e alla Geometria, Note di Matematica, IX-Suppl., 1989, pp. 59-71.
,[25] Alcuni Problemi Variazionali della Geometria, Conference in onore di G. Aquaro, Bari, Italy, 9 Nov. 1990, 1991, pp. 112-125, Conferenze del Sem. Mat. Bari.
,[26] Frontiere Orientate di Misura Minima e Questioni Collegate, Quaderni della Classe di Scienze della Scuola Normale Superiore di Pisa, Pisa, 1972. | MR 493669 | Zbl 0296.49031
, and ,[27] Convex Analysis and Variational Problems, North-Holland, New York, 1976. | MR 463994 | Zbl 0322.90046
and ,[28] Geometric Measure Theory, Springer-Verlag, Berlin, 1968. | MR 257325 | Zbl 0176.00801
,[29] L2-Lower Semicontinuity of Functionals of Quadratic Type, Ann. di Mat. Pura e Appl., Vol. 129, 1981, pp. 305-326. | MR 648337 | Zbl 0483.49008
and ,[30] Minimal Surfaces and Functions of Bounded Variation, Birkhäuser, Boston, 1984. | MR 775682 | Zbl 0545.49018
,[31] Sublinear Functions of Measures and Variational Integrals, Duke Math. J., Vol. 31, 1964, pp. 159-178. | MR 162902 | Zbl 0123.09804
and ,[32] The Gibbs-Thomson Relation within the Gradient Theory of Phase Transitions, Arch. Rat. Mech. An, Vol. 1, 1989, pp. 71-83. | MR 1000224 | Zbl 0681.49012
and ,[33] Minimal Surfaces of Codimension One, North-Holland, New York, 1984. | MR 795963 | Zbl 0565.49030
and ,[34] Sobolev Spaces, Springer-Verlag, Berlin, 1985. | MR 817985 | Zbl 0692.46023
,[35] Superfici Cartesiane Generalizzate ed Insiemi di Perimetro Localmente Finito sui Prodotti Cartesiani, Ann. Scuola Norm. Sup., Pisa, Vol. 3, 1964, pp. 515- 542. | Numdam | MR 174706 | Zbl 0152.24402
,[36] Multiple Integrals in the Calculus of Variations, Springer-Verlag, Berlin, 1966. | MR 202511 | Zbl 0142.38701
,[37] Bases Mathématiques du Calcul des Probabilités, Masson, Paris, 1980. | Zbl 0203.49901
,[38] Non Convex Variational Problems with General Singular Perturbations, Trans. Am. Math. Soc. Vol. 310, 1988, pp. 393-404. | Zbl 0718.34075
,[39] Non Convex Variational Problems with Anisotropic Perturbations, Nonlin. Anal., Vol. 16, 1991, pp. 705-719. | Zbl 0748.49034
and ,[40] La Méthode Métrique en Calcul des Variations, Hermann, Paris, 1941. | MR 12736 | Zbl 0027.10502
,[41] Weak Convergence of Completely Additive Vector Functions on a Set , Siberian Math. J., Vol. 9, 1968, pp. 1039-1045. | Zbl 0176.44402
,[42] Die Innere Geometrie der Metrischen Räume, Springer-Verlag, Berlin, 1961. | MR 123969 | Zbl 0096.16302
,[43] Convex Analysis, Princeton University Press, Princeton, New Jersey, 1972. | MR 1451876 | Zbl 0193.18401
,[44] The Index of Signature Operators on Lipschitz Manifolds, Inst. Hautes Études Sci. Publ. Math., Vol. 58, 1983, pp. 39-78. | Numdam | MR 720931 | Zbl 0531.58044
,[45] Derivations of Distance Functions on Rn, preprint, 1993.
,[46] The Space BV and Quasilinear Equation, Math. USSR Sbornik, Vol. 2, 1967, pp. 225-267. | Zbl 0168.07402
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