Korn’s constant for a spherical shell

Abstract

Upon invoking the variational characterization of Korn’s constant and Dafermos’ technique to reduce it to a boundary value problem, the Korn constant of a spherical shell of arbitrary thickness has been evaluated. The classical result of Payne and Weinberger for the sphere is recovered as the special case of vanishing interior radius, while as the thickness of the shell tends to zero, Korn’s constant tends to infinity in a nonuniform sense.