Stability of Trace Theorems on the Sphere

Neal Bez, Chris Jeavons, Tohru Ozawa, Mitsuru Sugimoto

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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 Lq 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.

Original languageEnglish
Pages (from-to)1456-1476
Number of pages21
JournalJournal of Geometric Analysis
Volume28
Issue number2
DOIs
Publication statusPublished - 2018 Apr 1

Keywords

  • Duality
  • Stability estimates
  • Trace theorems

ASJC Scopus subject areas

  • Geometry and Topology

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