Symbolic Calculus for Boundary Value Problems on a Manifold

In this chapter, following Fujiwara–Uchiyama (J. Math. Soc. Jpn. 23:625–635, 1971) we calculate precisely and explicitly the symbol of the Laplace–Beltrami operator \(\Delta _{\varOmega }\) near the boundary \(\partial \varOmega \) .