The Laplacian with Boundary Conditions

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


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. 1.Department of MathematicsEmory UniversityAtlantaUSA

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