Stability of trace theorems on the sphere

2016/11/03 by Bez, Neal, Jeavons, Chris, Ozawa, Tohru +1
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.00928

Abstract

We prove stable versions of trace theorems on the sphere in L² with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into L^q for q > 2, by combining a refined Hardy-Littlewood-Sobolev inequality on the sphere with a duality-stability result proved very recently by Carlen. Finally, we extend a local version of Carlen's duality theorem to establish local stability of certain Strichartz estimates for the kinetic transport equation.

Related

• Extremisers for the trace theorem on the sphere
• Sharp One-bubble Critical-Point Stability and Global Compactness for the Sobolev Trace Inequality
• Sharp Gradient Stability for the Sobolev Trace Inequality
• Optimality and stability of the radial shapes for the Sobolev trace constant
• Sharp kinetic trace theory