(eng): An optimal design problem for a plate governed by a linear, elliptic equation with bounded thickness varying only in a single prescribed direction and with unilateral isoperimetrical-type constraints is considered. Using Murat-Tartar's homogenization theory for stratified plates and Young-measure relaxation theory, smoothness of the extended cost and constraint functionals is proved, and then the maximum principle necessary for an optimal relaxed design is derived.

(cze): V práci se odvozuje princip maxima v optimálním návrhu desek s laminátově uspořádanou tloušťkou.