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Weak notions of Jacobian determinant and relaxation. (English) Zbl 1242.49025
Summary: We study two weak notions of the Jacobian determinant for Sobolev maps, namely the distributional Jacobian and the relaxed total variation, which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals.

49J45 Methods involving semicontinuity and convergence; relaxation
28A75 Length, area, volume, other geometric measure theory
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