Bounds for eigenfunctions of the Neumann p-Laplacian on noncompact Riemannian manifolds

Abstract

Abstract Eigenvalue problems for the p -Laplace operator in domains with finite volume, on noncompact Riemannian manifolds, are considered. If the domain does not coincide with the whole manifold, Neumann boundary conditions are imposed. Sharp assumptions ensuring L q {L^{q}} - or L ∞ {L^{\infty}} -bounds for eigenfunctions are offered either in terms of the isoperimetric function or of the isocapacitary function of the domain.