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<p>In this work, we are interested in studying Serrin’s overdetermined problems in Riemannian manifolds. For manifolds endowed with a conformal vector field, we prove a Pohozaev-type identity to establish a Serrin-type rigidity result using the <i>P</i>-function approach introduced by Weinberger. To achieve this, we proceed with a conformal change, starting from a geometric identity due to Schoen. Moreover, we obtain a symmetry result for the associated Dirichlet problem by utilizing a generalized normalized wall shear stress bound.</p>

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Rigidity results for Serrin’s overdetermined problems in Riemannian manifolds

  • 期刊论文

  • 发表日期：

    2025年3月24日

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  • Maria Andrade,
  • Allan Freitas,
  • Diego A. Marín

摘要

In this work, we are interested in studying Serrin’s overdetermined problems in Riemannian manifolds. For manifolds endowed with a conformal vector field, we prove a Pohozaev-type identity to establish a Serrin-type rigidity result using the P-function approach introduced by Weinberger. To achieve this, we proceed with a conformal change, starting from a geometric identity due to Schoen. Moreover, we obtain a symmetry result for the associated Dirichlet problem by utilizing a generalized normalized wall shear stress bound.