 ##  [Poincaré Inequality](/poincare-inequality) 

  ##  [Poincaré Inequality](https://natural.quantumdictionary.io/poincare-inequality-0) 

  
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**Natural &amp; Formal Sciences Dictionary**

 
Definition

An inequality that bounds the L^p norm of a function (after removing a rigid mode such as mean or boundary trace) by the L^p norm of its gradient on a domain, exhibiting that gradients control function oscillation up to constants.

 
 ##  [Poincaré Inequality](https://mathlogic.quantumdictionary.io/poincare-inequality-1) 

  
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- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

An inequality that bounds the L2 norm of a function (after subtracting an appropriate mean or enforcing boundary conditions) by a constant times the L2 norm of its gradient on a domain, quantifying how oscillation is controlled by first derivatives.