Source: Duke Math. J.
Volume 67, Number 3
[AMT] L. Ambrosio, S. Mortola, and V. M. Tortorelli, Functionals with linear growth defined on vector valued BV functions, J. Math. Pures Appl. (9) 70 (1991), no. 3, 269–323.
[AG1] P. Aviles and Y. Giga, Variational integrals on mappings of bounded variation and their lower semicontinuity, Arch. Rational Mech. Anal. 115 (1991), no. 3, 201–255.
[AG2] P. Aviles and Y. Giga, Minimal currents and relaxation of variational integrals on mappings of bounded variation, Proc. Japan Acad. Ser. A Math. Sci. 66 (1990), no. 3, 68–71.
[Ba] S. Baldo, Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), no. 2, 67–90.
[BBC] F. Bethuel, H. Brezis, and J.-M. Coron, Relaxed energies for harmonic maps, Variational methods (Paris, 1988) eds. H. Berestycki, J. M. Coron, and I. Ekeland, Progr. Nonlinear Differential Equations Appl., vol. 4, Birkhäuser Boston, Boston, MA, 1990, pp. 37–52.
[Bo] M. E. Bogovski, Solution of the first boundary value problem for the equation of continuity of an incompressible medium, Soviet Math. Dokl. 20 (1979), 1094–1098.
Mathematical Reviews (MathSciNet): MR553920
[BS] W. Borchers and H. Sohr, On the equations $\rm rot\,\bf v=\bf g$ and $\rm div\,\bf u=f$ with zero boundary conditions, Hokkaido Math. J. 19 (1990), no. 1, 67–87.
[D] B. Dacorogna, Quasiconvexity and relaxation of nonconvex problems in the calculus of variations, J. Funct. Anal. 46 (1982), no. 1, 102–118.
[DM] G. Dal Maso, Integral representation on $\rm BV(\Omega )$ of $\Gamma$-limits of variational integrals, Manuscripta Math. 30 (1979/80), no. 4, 387–416.
[DG] E. De Giorgi, $G$-operators and $\Gamma$-convergence, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) eds. Z. Ciesielski and C. Olech, PWN, Warsaw, 1984, pp. 1175–1191.
[F1] H. Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969.
[F2] H. Federer, Real flat chains, cochains and variational problems, Indiana Univ. Math. J. 24 (1974/75), 351–407.
[FR] I. Fonseca and P. Rybka, Relaxation of multiple integrals in the space $BV(\Omega,\mathbbR^p)$, preprint.
[FT] I. Fonseca and L. Tartar, The gradient theory of phase transitions for systems with two potential wells, Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), no. 1-2, 89–102.
[GMS1]1 M. Giaquinta, G. Modica, and J. Souček, Functionals with linear growth in the calculus of variations. I, Comment. Math. Univ. Carolin. 20 (1979), no. 1, 143–156.
[GMS1]2 M. Giaquinta, G. Modica, and J. Souček, Functionals with linear growth in the calculus of variations. II, Comment. Math. Univ. Carolin. 20 (1979), no. 1, 157–172.
[GMS2] M. Giaquinta, G. Modica, and J. Souček, The Dirichlet energy of mappings with values into the sphere, Manuscripta Math. 65 (1989), no. 4, 489–507.
[Giu] E. Giusti, Minimal surfaces and functions of bounded variation, Monographs in Mathematics, vol. 80, Birkhäuser Verlag, Basel, 1984.
[GS] C. Goffman and J. Serrin, Sublinear functions of measures and variational integrals, Duke Math. J. 31 (1964), 159–178.
Mathematical Reviews (MathSciNet): MR29:206
[I] M. Iri, Network flow, transportation and scheduling, Mathematics in Science and Engineering, Vol. 57, Academic Press, New York, 1969.
[JK] R. James and D. Kinderlehrer, Theory of diffusionless phase transitions, PDEs and continuum models of phase transitions (Nice, 1988) eds. M. Rascle, D. Serre, and M. Slemord, Lecture Notes in Phys., vol. 344, Springer, Berlin, 1989, pp. 51–84.
[M1] L. Modica, The gradient theory of phase transitions and the minimal interface criterion, Arch. Rational Mech. Anal. 98 (1987), no. 2, 123–142.
[Mor] F. Morgan, Area-minimizing currents bounded by higher multiples of curves, Rend. Circ. Mat. Palermo (2) 33 (1984), no. 1, 37–46.
[Re] Ju. G. Rešetnjak, The weak convergence of completely additive vector-valued set functions, Sibirsk. Mat. Ž. 9 (1968), 1386–1394, Siberian Math. J. 9, (1986), 1039–1045.
[Ro] R. T. Rockafellar, Dual problems of Lagrange for arcs of bounded variation, Calculus of variations and control theory (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1975; dedicated to Laurence Chisholm Young on the occasion of his 70th birthday) ed. D. L. Russel, Academic Press, New York, 1976, 155–192. Publ. Math. Res. Center Univ. Wisconsin, No. 36.
[Se1] J. Serrin, A new definition of the integral for nonparametric problems in the calculus of variations, Acta Math. 102 (1959), 23–32.
[Se2] J. Serrin, On the definition and properties of certain variational integrals, Trans. Amer. Math. Soc. 101 (1961), 139–167.
[Si] L. Simon, Lectures on geometric measure theory, Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 3, Australian National University Centre for Mathematical Analysis, Canberra, 1983.
[St1] P. Sternberg, The effect of a singular perturbation on nonconvex variational problems, Arch. Rational Mech. Anal. 101 (1988), no. 3, 209–260.
[St2] P. Sternberg, Vector-valued local minimizers of nonconvex variational problems, Rocky Mountain J. Math. 21 (1991), no. 2, 799–807.
[W] B. White, The least area bounded by multiples of a curve, Proc. Amer. Math. Soc. 90 (1984), no. 2, 230–232.
[Y] L. C. Young, Some extremal questions for simplicial complexes. IV. The algebraic and the geometric resultant, and application of variational methods, Rend. Circ. Mat. Palermo (2) 12 (1963), 200–210.