Korn's inequality for periodic solids and convergence rate of homogenization
Giuseppe Cardone, Antonio Corbo Esposito, С. А. Назаров · Applicable Analysis · 2009
In a three-dimensional solid with arbitrary periodic Lipschitz perforation the Korn inequality is proved with a constant independent of the perforation size. The convergence rate of homogenization as a function of the Sobolev–Slobodetskii smoothness of data is also estimated. We improve foregoing results in elasticity dropping customary restrictions on the shape of the periodicity cell and superfluous smoothness and smallness assumptions on the external forces and traction.