Laplacian in whole space or in a domain with boundaries
Partial differential equations

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AF190 V1 Article

Laplacian in whole space or in a domain with boundaries
Partial differential equations

Authors : Claude BARDOS, Thierry PAUL

Publication date: October 10, 2010 | Lire en français

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

3.1 Introduction to the Laplacian

In Rn, the Laplacian is the operator

Δ=∑1≤i≤n∂2∂xi2.

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 phenomena), and so on. This is partly due to the fact that...

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