Korn type inequalities in Orlicz spaces

We exhibit balance conditions between a Young function A and a Young function B for a Korn type inequality to hold between the L^B norm of the gradient of vector-valued functions and the L^A norm of its symmetric part. In particular, we extend a standard form of the Korn inequality in L^p, and an Orlicz version involving a Young function A satisfying both the Delta_2 and the nabla_2 condition. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.