Boundary pairs associated with quadratic forms. Issue 8 (10th December 2015)

• Record Type: Journal Article
• Authors: Post, Olaf
• Is Part Of: Mathematische Nachrichten. Volume 289:Issue 8/9(2016)
• Page Start: 1052
• Page End: 1099
• Publication Date: 2015-12-10
• Subjects: Boundary triples -- abstract boundary value problems -- abstract Dirichlet problem -- variational Dirichlet‐to‐Neumann operator -- Krein‐type resolvent formulas -- spectral characterisation -- Zaremba problem -- 47A10 -- 47B65 -- 47F05 -- 35J25; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201500048
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract : We introduce a purely functional analytic framework for elliptic boundary value problems in a variational form. We define abstract Neumann and Dirichlet boundary conditions and a corresponding Dirichlet‐to‐Neumann operator, and develop a theory relating resolvents and spectra of these operators. We illustrate the theory by many examples including Jacobi operators, Laplacians on spaces with (non‐smooth) boundary, the Zaremba (mixed boundary conditions) problem and discrete Laplacians.