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Some remarks on the distributional Jacobian. (English) Zbl 1025.49030
In [Indiana Univ. Math. J. 51, No. 3, 645-677 (2002)] J. L. Jerrard and H. M. Soner proved a “weak” co-area formula involving distributional Jacobians. The author now proves a “strong” co-area type formula based on a chain rule for distributional Jacobians of some classes of maps.

MSC:
49Q20 Variational problems in a geometric measure-theoretic setting
49J10 Existence theories for free problems in two or more independent variables
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[1] Ambrosio, L.; Fusco, N.; Pallara, D., Functions of bounded variation and free discontinuity problems, (2000), Clarendon Press Oxford · Zbl 0957.49001
[2] Ambrosio, L.; Kirchheim, B., Currents on metric spaces, Acta math., 185, 1-80, (2000) · Zbl 0984.49025
[3] Brezis, H.; Nirenberg, L., Degree theory and bmopart 1, compact manifolds without boundaries, Selecta math. (N.S.), 1, 197-263, (1995) · Zbl 0852.58010
[4] Dacorogna, B.; Moser, J., On a partial differential equation involving the Jacobian determinant, Ann. inst. H. poincare anal. non lineare, 7, 1-26, (1990) · Zbl 0707.35041
[5] De Lellis, C., Fine properties of currents and applications to distributional Jacobians, Proc. roy. soc. Edinburgh, 132A, 815-842, (2002) · Zbl 1025.49029
[6] Federer, H., Geometric measure theory, (1969), Springer Berlin · Zbl 0176.00801
[7] Giaquinta, M.; Modica, G.; Souček, J., Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity, Arch. rational mech. anal, 106, 97-159, (1989) · Zbl 0677.73014
[8] Giaquinta, M.; Modica, G.; Souček, J., Cartesian currents in the calculus of variations, (1998), Springer Berlin · Zbl 0914.49001
[9] Jerrard, L.; Soner, M., Functions of higher bounded variation, Indiana univ. math. J., 51, 645-677, (2002) · Zbl 1057.49036
[10] Marcus, M.; Mizel, V.J., Transformations by functions in Sobolev spaces and lower semicontinuity for parametric variational integrals, Bull. amer. math. soc., 79, 790-795, (1973) · Zbl 0275.49041
[11] Müller, S.; Spector, S., An existence theory for nonlinear elasticity that allows for cavitation, Arch. rational mech. anal., 131, 1-66, (1995) · Zbl 0836.73025
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