Partial regularity for certain classes of polyconvex functionals related to nonlinear elasticity

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.