We investigate the character of the linear constraints which are needed for Poincaré and Korn type inequalities to hold. We especially analyze constraints which depend on restriction on subsets of positive measure and on the trace on a portion of the boundary.
In this paper we review some recent results concerning
inverse problems for thin elastic plates. The plate is assumed to
be made by non-homogeneous linearly elastic material belonging to
a general class of anisotropy. A first group of results concerns
uniqueness and stability for the determination of unknown
boundaries, including the cases of cavities and rigid inclusions.
In the second group of results, we consider upper and lower
estimates of the area of unknown inclusions given in terms of the
work exerted by a couple field applied at the boundary of the
plate. In particular, we extend previous size estimates for
elastic inclusions to the case of cavities and rigid inclusions.