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

In this paper, we obtain two rigidity results for ‐Laplace type equation and ‐Laplace equation with exponential nonlinearity on ‐dimensional compact Riemannian manifolds by using of nonlinear flow and the carré du champ methods, respectively, where rigidity means that the PDE has only constant solut...

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Published in:Mathematical methods in the applied sciences 2023-11, Vol.46 (17), p.18420-18432
Main Authors: Wang, Yu‐Zhao, Wei, Pei‐Can, Zhang, Huiting
Format: Article
Language:English
Subjects:
Interpolation
Laplace equation
Nonlinearity
Riemann manifold
Rigidity
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Wei, Pei‐Can
Zhang, Huiting
description In this paper, we obtain two rigidity results for ‐Laplace type equation and ‐Laplace equation with exponential nonlinearity on ‐dimensional compact Riemannian manifolds by using of nonlinear flow and the carré 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.
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subjects Interpolation
Laplace equation
Nonlinearity
Riemann manifold
Rigidity
title Rigidity results for the p ‐Laplace type equations on compact Riemannian manifolds
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