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In this paper we analyze some properties of a sixth order elliptic operatorarising in the framework of the strain gradient linear elasticity theory fornanoplates in flexural deformation. We first rigorously deduce the weakformulation of the underlying Neumann problem as well as its well posedness.Under some suitable smoothness assumptions on the coefficients and on thegeometry we derive interior and boundary regularity estimates for the solutionof the Neumann problem. Finally, for the case of isotropic materials, we obtainnew Strong Unique Continuation results in the interior, in the form of doublinginequality and three spheres inequality, by a Carlemann estimates approach.

Strong unique continuation and global regularity estimates for nanoplates