Critical Points of Degenerate Polyconvex Energies

We study critical and stationary, i.e., with respect to both inner outer variations, points of polyconvex functionals the form for . In particular, we show that a.e. have locally constant determinant except in a relatively closed set measure zero, stationary almost everywhere. This is deduced from more general result concerning solutions , linearized problem also present some generalization original higher dimensions assuming further regularity on Finally, differential inclusion associated stationarity energies as above rigid.