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Sharp constants in weighted trace inequalities on Riemannian manifolds

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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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