##  [Nash Inequality](/index.php/nash-inequality) 

  ##  [Nash Inequality](https://mathlogic.quantumdictionary.io/nash-inequality-0) 

  

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**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A functional inequality that relates the L2 norm of a function to its L1 norm and its Dirichlet energy (L2 norm of the gradient), typically taking the form ||f||_2^{2+4/n} ≤ C ||∇f||_2^2 ||f||_1^{4/n} on R^n, and used to derive decay and smoothing estimates for the heat equation and semigroups.