Qualitative properties of bounded subsolutions of nonlinear PDEs

2020/01/16 by Bianchi, Davide, Pigola, Stefano, Setti, Alberto G. · 1 citation
#31B35 #53C21 #58J05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.05756

Abstract

We study decay and compact support properties of positive and bounded solutions of Δ_p u ≥ Λ(u) on the exterior of a compact set of a complete manifold with rotationally symmetry. In the same setting, we also give a new characterization of stochastic completeness for the p-Laplacian in terms of a global W^1,p-regularity of such solutions. One of the tools we use is a nonlinear version of the Feller property which we investigate on general Riemannian manifolds and which we establish under integral Ricci curvature conditions.

Cited by

• p-eigenvalue pinching sphere theorems

Related

• Stochastic Properties of the Laplacian on Riemannian Submersions
• The Feller property on Riemannian manifolds
• Propagation of low regularity for solutions of nonlinear PDEs on a Riemannian manifold with a sub-Laplacian structure
• Nonlinear characterizations of stochastic completeness
• Growth of subsolutions of Δ_p u = V|u|^p-2u and of a general class of quasilinear equations