##  [Korn's Inequality](/korns-inequality) 

  ##  [Korn's Inequality](https://engineering.quantumdictionary.io/korns-inequality-0) 

  

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**Engineering & Applied Technologies Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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).