This is one of Green's
identities for the Laplacian, which is really just a
sophisticated version of integration by parts. Here M
can be a Riemannian manifold with boundary, or simply a bounded
domain in the plane or in space.
REFERENCES:
Thomas
Apostol, Calculus, Volume 2, Second Edition, New
York, Wiley, 1969, page 386.
John M. Lee, Riemannian
Manifolds: An Introduction to Curvature, New York,
Springer-Verlag, 1997, page 44.
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