Stability of Trace Theorems on the Sphere

Neal Bez, Chris Jeavons, Tohru Ozawa, Mitsuru Sugimoto

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    We prove stable versions of trace theorems on the sphere in (Formula presented.) with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into (Formula presented.) for (Formula presented.), 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)1-21
    Number of pages21
    JournalJournal of Geometric Analysis
    DOIs
    Publication statusAccepted/In press - 2017 Jun 1

    Fingerprint

    Trace Theorem
    Optimal Constants
    Strichartz Estimates
    Duality Theorems
    Local Stability
    Kinetic Equation
    Transport Equation

    Keywords

    • Duality
    • Stability estimates
    • Trace theorems

    ASJC Scopus subject areas

    • Geometry and Topology

    Cite this

    Stability of Trace Theorems on the Sphere. / Bez, Neal; Jeavons, Chris; Ozawa, Tohru; Sugimoto, Mitsuru.

    In: Journal of Geometric Analysis, 01.06.2017, p. 1-21.

    Research output: Contribution to journalArticle

    Bez, Neal ; Jeavons, Chris ; Ozawa, Tohru ; Sugimoto, Mitsuru. / Stability of Trace Theorems on the Sphere. In: Journal of Geometric Analysis. 2017 ; pp. 1-21.
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