We obtain the best constant in Korn’s inequality for solenoidal vector fields on a periodic slab which vanish on a part of its boundary. To do this we consider the Stokes equations with Dirichlet boundary conditions, following H. Ito ,.
"Optimal Korn’s inequality for solenoidal vector fields on a periodic slab." Proc. Japan Acad. Ser. A Math. Sci. 88 (10) 168 - 172, December 2012. https://doi.org/10.3792/pjaa.88.168