The Jump of the Laplacian on a Submanifold

Assume that a submanifold M ⊂ ℝ n of an arbitrary codimension k ϵ {1, …, n } is closed in some open set O →ℝ n . With a given function u ϵ C 2 ( O \ M ) we may associate its trivial extension u : O →ℝ such that u| O \M = u and u| m ≡ 0. The jump of the Laplacian of the function u on the submanifold M is defined by the distribution Δ u — Δ u . By applying some general version of the Fubini theorem to the nonlinear projection onto M we obtain the formula for the jump of the Laplacian (Theorem 2.2).