Strongly M-elliptic proper uniform pseudo-differential operators and generation of holomorphic semigroups in Lp-spaces on non-compact manifolds

Abstract

Let X be a manifold of bounded geometry. We study proper uniform pseudo-differential operators on X, whose coordinate representations have symbols belonging to a weighted class introduced by Garello and Morando. We provide sufficient conditions ensuring that a proper uniform pseudo-differential operator A on X generates a holomorphic semigroup in (Formula presented.), (Formula presented.). Consequently, we get that the Cauchy problem for an evolution equation in (Formula presented.), (Formula presented.), ‘driven’ by A, is well-posed.