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In this paper we consider Lipschitz graphs of functions which are stationarypoints of strictly polyconvex energies. Such graphs can be thought as integralcurrents, resp. varifolds, which are stationary for some elliptic integrands.The regularity theory for the latter is a widely open problem, in particular nocounterpart of the classical Allard's theorem is known. We address the issuefrom the point of view of differential inclusions and we show that the relevantones do not contain the class of laminates which are used in [22] and [25] toconstruct nonregular solutions. Our result is thus an indication that anAllard's type result might be valid for general elliptic integrands. Weconclude the paper by listing a series of open questions concerning theregularity of stationary points for elliptic integrands.

Geometric measure theory and differential inclusions