Rigidity results for the $p$-Laplace type equations on compact Riemannian manifolds

Yu-Zhao Wang; Pei-Can Wei; Huiting Zhang

Rigidity results for the $p$-Laplace type equations on compact Riemannian manifolds

Analysis of PDEs 2023-05-23 v3 Differential Geometry

Authors: Yu-Zhao Wang , Pei-Can Wei , Huiting Zhang

Abstract

In this paper, we obtain two rigidity results for $p$ -Laplace type equation and $n$ -Laplace equation with exponential nonlinearity on $n$ -dimensional compact Riemannian manifolds by using of nonlinear flow and the carr\'e du champ methods, respectively, where rigidity means that the PDE has only constant solution when a parameter is in a certain range. Moreover, an interpolation inequality is derived as an application.

Keywords

rigidity p-laplace equation n-laplace equation compact riemannian manifold exponential nonlinearity interpolation inequality

Cite

@article{arxiv.1904.02568,
  title  = {Rigidity results for the $p$-Laplace type equations on compact Riemannian manifolds},
  author = {Yu-Zhao Wang and Pei-Can Wei and Huiting Zhang},
  journal= {arXiv preprint arXiv:1904.02568},
  year   = {2023}
}

Comments

There is an error in lemma 2.2

Rigidity results for the $p$-Laplace type equations on compact Riemannian manifolds

Abstract

Keywords

Cite

Comments

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