# reference request: elliptical regularity in compact manifold without limit

Leave $$(M, g)$$ be a compact Riemannian collector without limit, and $$Delta$$ is the operator of Laplace-Beltrami in $$M$$. Is there any result in elliptical regularity like this:

For any $$u in H ^ 1 (M)$$Y $$f in L ^ 2 (M)$$ such that $$Delta u = f$$ (in the sense of distributions), then $$u in H ^ 2 (M)$$.
If there is a good reference for that result of regularity, it would be good.