Korn type inequalities in Orlicz spaces

摘要

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 func-tions and the L~A norm of its symmetric part. In particular, we extend a standard form of the Korn inequality in L~p, with 1 <∞, and an Orlicz version involving a Young function Asatisfying both the Δ_2 and the ?_2 condition.