Korn's Inequality

A family of functional inequalities in Sobolev spaces that bounds the L2 norm of the full gradient of a displacement field by the L2 norm of its symmetric part (the linearized strain) up to rigid‑body motions: there exists a constant C (depending on the domain and boundary conditions) such that ||∇u||_{L2} ≤ C (||ε(u)||_{L2} + lower‑order terms).