Abstract
Consider the variational integral\(J(u): = \mathop \smallint \limits_\Omega \left| {\nabla u} \right|^p + H(\det \nabla u) dx\) where Ω⊂ℝn andp≥n≥2. H: (0, ∞)→[0, ∞) is a smooth convex function such that\(\mathop {\lim }\limits_{t \downarrow 0} H(t) = \infty \). We approximateJ by a sequence of regularized functionalsJ δ whose minimizers converge strongly to anJ-minimizing function and prove partial regularity results forJ δ-minimizers.
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Fuchs, M., Reuling, J. Partial regularity for certain classes of polyconvex functionals related to nonlinear elasticity. Manuscripta Math 87, 13–26 (1995). https://doi.org/10.1007/BF02570458
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DOI: https://doi.org/10.1007/BF02570458