THE JUMP OF THE LAPLACIAN ON A SUBMANIFOLD

Assume that a submanifold M subset of IRn of an arbitrary codimension k is an element of {1,...,n} is closed in some open set O subset of IR n. With a given function u is an element of C-2(O\M) we may associate its trivial extension (u) over bar : O --> IR such that (u) over bar\( O/M) = u and (u) over bar\(M) = 0. The jump of the Lapracian of the fu nction u, on the submanifold M is defined by the distribution Delta (u ) over bar - <(Delta)over bar>u. By applying some general version of t he Fubini theorem to the nonlinear projection onto M we obtain the for mula for the jump of the Laplacian (Theorem 2.2).