Abstract

In this paper, we find optimal constants of a special class of Gagliardo-Nirenberg type inequalities which turns out to interpolate between the classical Sobolev inequality and the Gross logarithmic Sobolev inequality. These inequalities provide an optimal decay rate (measured by entropy methods) of the intermediate asymptotics of solutions to nonlinear diffusion equations. © 2002 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.