3. Laplacian in whole space or in a domain with boundaries

3.1 Introduction to the Laplacian

In R ⁿ , the Laplacian is the operator

Δ= \sum_{1 \leq i \leq n} \frac{\partial^{2}}{\partial x_{i}^{2}} .

This operator, already introduced as an essential element of the Schrödinger equation, also appears in geometry, physics (in addition to quantum physics, in the description of macroscopic...

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Laplacian in whole space or in a domain with boundaries

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References

(1) - ARNOL'D (V.) - Méthodes mathématiques de la mécanique classique - MIR, Moscou (1976).
(2) - ALINHAC (S.), GERARD (P.) - Opérateurs pseudo-différentiels et théorème de Nash-Moser - InterÉditions-CNRS, Paris (1991).
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