On m-Accretivity of Perturbed Bochner Laplacian in L p Spaces on Riemannian Manifolds

Abstract

We consider a differential expression $${H=\nabla^*\nabla+V}$$ , where $${\nabla}$$ is a Hermitian connection on a Hermitian vector bundle E over a manifold of bounded geometry (M, g) with metric g, and V is a locally integrable section of the bundle of endomorphisms of E. We give a sufficient condition for H to have an m-accretive realization in the space L p (E), where 1 < p < +∞. We study the same problem for the operator Δ M + V in L p (M), where 1 < p < ∞, Δ M is the scalar Laplacian on a complete Riemannian manifold M, and V is a locally integrable function on M.