The Regularity of Critical Points of Polyconvex Functionals

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Regularity of minima: An invitation to the dark side of the calculus of variations (2006, background): “The work of Müller & ˇ Sverák is nowadays generating massive developments: let me mention the remarkable extension of their results to the case of polyconvex functionals by Székelyhidi [292], using this time " T 5 -configurations " ; see also [293] for a striking two-dimensional result.”
Conformal representation of surfaces, and Plateau's problem for Cartan functionals (2005, background): “Sźekelyhidi [53] improved this result in the following way: There exists a smooth, strongly polyconvex f(p) on R2 × R2 with bounded second derivatives such that the elliptic system in divergence form divfp(∇X) = 0 admits weak solutions X ∈ Lip(B,R2) on the unit ballB of R2 which are notC1 in any (no”
The Singular Set of Lipschitzian Minima of Multiple Integrals (2007, background): “17) That the situation is equally hopeless when the above quasiconvexity condition on the integrand F is strengthened to polyconvexity was demonstrated more recently by Székelyhidi in [39].”