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Sharp constants in weighted trace inequalities on Riemannian manifolds

Calculus of Variations and Partial Differential Equations volume 48, pages 555–585 (2013)Cite this article

Abstract

In this paper, we establish some sharp weighted trace inequalities \({W^{1,2}(\rho^{1-2 \sigma}, M) \hookrightarrow L^{\frac{2n}{n-2 \sigma}}(\partial M)}\) on n + 1 dimensional compact smooth manifolds with smooth boundaries, where ρ is a defining function of M and \({\sigma \in (0,1)}\) . This is stimulated by some recent work on fractional (conformal) Laplacians and related problems in conformal geometry, and also motivated by a conjecture of Aubin.

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ, 08854, USA

    Tianling Jin & Jingang Xiong

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Jingang Xiong

Authors
  1. Tianling Jin
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  2. Jingang Xiong
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Correspondence to Tianling Jin.

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Communicated by O. Savin.

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Jin, T., Xiong, J. Sharp constants in weighted trace inequalities on Riemannian manifolds. Calc. Var. 48, 555–585 (2013). https://doi.org/10.1007/s00526-012-0562-8

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  • DOI: https://doi.org/10.1007/s00526-012-0562-8

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