The Jump of the Laplacian on a Submanifold
Ewa Dudek, Konstanty Holly · Mathematische Nachrichten · 1997
Abstract Assume that a submanifold M ⊂ ℝn of an arbitrary codimension k ϵ {1, …, n} is closed in some open set O→ℝn. With a given function u ϵ C2(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 Δu — Δu. 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).