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The Laplacian with Boundary Conditions

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Spectral Theory

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 284))

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Abstract

The abstract theory developed in previous chapters is applied to the spectral theory of the Laplacian on a bounded open set in Euclidean space. We define the sefl-adjoint extensions corresponding to classical boundary conditions. The chapter includes discussion of some classic spectral results, including the Weyl law, Courant’s nodal domain theorem, and eigenvalue comparison theorems.

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Authors and Affiliations

  1. Department of Mathematics, Emory University, Atlanta, GA, USA

    David Borthwick

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  1. David Borthwick
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Borthwick, D. (2020). The Laplacian with Boundary Conditions. In: Spectral Theory. Graduate Texts in Mathematics, vol 284. Springer, Cham. https://doi.org/10.1007/978-3-030-38002-1_6

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