On a new class of elastic deformations not allowing for cavitation

S. Müller; Tang Qi; B. S. Yan

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A characterization of the total variation $T V (u, Ω)$ of the Jacobian determinant $det D u$ is obtained for some classes of functions $u : Ω \to R^{n}$ outside the traditional regularity space $W^{1, n} (Ω; R^{n})$ . In particular, explicit formulas are deduced for functions that are locally Lipschitz continuous away from a given one point singularity $x_{0} \in Ω$ . Relations between $T V (u, Ω)$ and the distributional determinant $Det D u$ are established, and an integral representation is obtained for the relaxed energy of certain polyconvex functionals at maps $u \in W^{1, p} (Ω; R^{n}) \cap W^{1, \infty} (Ω \{x_{0}\}; R^{n})$ . ...

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