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

Abstract

In this paper, we obtain two rigidity results for p-Laplacian type equations on compact Riemannian manifolds by using of the carré du champ and nonlinear flow 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.