A Gagliardo-Nirenberg-type inequality and its applications to decay estimates for solutions of a degenerate parabolic equation

摘要

We establish a Gagliardo-Nirenberg-type inequality in R-n for functions which decay fast as vertical bar x vertical bar -> infinity. We use this inequality to derive upper bounds for the decay rates of solutions of a degenerate parabolic equation. Moreover, we show that these upper bounds, hence also the Gagliardo-Nirenberg-type inequality, are sharp in an appropriate sense. (C) 2019 Elsevier Inc. All rights reserved.