Lp-interpolation inequalities and global Sobolev regularity results (with an appendix by Ognjen Milatovic).

On any complete Riemannian manifold M and for all p∈[2,∞), we prove a family of second-order Lp-interpolation inequalities that arise from the following simple Lp-estimate valid for every u∈C∞(M): ‖∇u‖pp≤‖uΔpu‖1∈[0,∞],where Δp denotes the p-Laplace operator. We show that these inequalities, in combination with abstract functional analytic arguments, allow to establish new global Sobolev regularity results for Lp-solutions of the Poisson equation for all p∈(1,∞), and new global Sobolev regularity results for the singular magnetic Schrödinger semigroups. [ABSTRACT FROM AUTHOR]