2016/10/21 by Francis Seuffert, Seuffert, Francis
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1610.06869
openalex publication_date 2016/10/21 · openalex created_date 2016/11/04 · openalex updated_date 2026/07/28
In a recent paper, E. Carlen and A. Figalli prove a stability estimate - also known as a quantitative inequality - for a sharp Gagliardo-Nirenberg inequality and use this result to solve a Keller-Segal Equation. The Gagliardo-Nirenberg Inequality that Carlen and Figalli prove their stability estimate for is part of a larger family of sharp Gagliardo-Nirenberg inequalities, for which the sharp constants and extremals were identified in some cases by Carrillo and Toscani, and then for the remaining cases by Del Pino and Dolbeault. We prove a stability estimate for the entire family of sharp Gagliardo-Nirenberg inequalities for which Del Pino and Dolbeault calculated the sharp constants and extremals. Establishing stability estimates of inequalities is an active topic. A key piece of our proof is the application of a continuous dimension generalization of the Bianchi-Egnell Stability Estimate proven by the author.