Nash Inequality

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.