The Jump of the Laplacian on a Submanifold
Copyright policy )The Jump of the Laplacian on a Submanifold
AbstractAssume 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).
- Jagiellonian University Poland
nonlinear projection, Distributions, generalized functions, distribution spaces, integral calculus on Riemannian manifolds, distributions, jump of the Laplacian, Theory of singularities and catastrophe theory, nonlinear orthogonal projection, Integration on manifolds; measures on manifolds, Fubini theorem, Differentiable maps on manifolds, submanifold of an arbitrary codimension, Distance geometry
nonlinear projection, Distributions, generalized functions, distribution spaces, integral calculus on Riemannian manifolds, distributions, jump of the Laplacian, Theory of singularities and catastrophe theory, nonlinear orthogonal projection, Integration on manifolds; measures on manifolds, Fubini theorem, Differentiable maps on manifolds, submanifold of an arbitrary codimension, Distance geometry
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