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Sharp boundary trace theory and Schrödinger operators on bounded Lipschitz domains / Jussi Behrndt, Fritz Gesztesy, Marius Mitrea

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 307, number 1550 (March 2025)Publisher: Providence, RI : American Mathematical Society, March 2025Description: vi, 208 SeitenISBN:
  • 9781470472672
Subject(s): Additional physical formats: No title | 9781470480912 | Erscheint auch als: Sharp boundary trace theory and Schrödinger operators on bounded Lipschitz domains. Online-Ausgabe Providence, RI : American Mathematical Society, 2025. 1 Online-Ressource (vi, 208 Seiten)MSC: MSC: 35J25 | 35J40 | 35P15 | 35P05 | 46E35 | 47A10 | 47F05 | 35J25RVK: RVK: SI 130LOC classification:
  • QC20.7.F84
Summary: Keywords: Lipschitz domains, nontangential maximal function, nontangential boundary trace, Sobolev space, Besov space, Triebel–Lizorkin space, Dirichlet trace, Neumann trace, Dirichlet Laplacian, Neumann Laplacian, Krein Laplacian, Schrödinger operator, Friedrichs extension, self-adjoint extensions, eigenvalues, spectral analysis, Weyl asymptotics, buckling problem, Riemannian manifold, Laplace–Beltrami operatorSummary: "We develop a sharp boundary trace theory in arbitrary bounded Lipschitz domains which, in contrast to classical results, allows "forbidden" endpoints and permits the consideration of functions exhibiting very limited regularity. This is done at the (necessary) expense of stipulating an additional regularity condition involving the action of the Laplacian on the functions in question which, nonetheless, works perfectly with the Dirichlet and Neumann realizations of the Schrodinger differential expression . In turn, this boundary trace theory serves as a platform for developing a spectral theory for Schrodinger operators on bounded Lipschitz domains, along with their associated Weyl-Titchmarsh operators. Overall, this pushes the present state of knowledge a significant step further. For example, we succeed in extending the Dirichlet and Neumann trace operators in such a way that all self-adjoint extensions of a Schrodinger operator on a bounded Lipschitz domain may be described with explicit boundary conditions, thus providing a final answer to a problem that has been investigated for more than 60 years in the mathematical literature. Along the way, a number of other open problems are solved. The most general geometric and analytic setting in which the theory developed here yields satisfactory results is that of Lipschitz subdomains of Riemannian manifolds and for the corresponding Laplace-Beltrami operator (in place of the standard flat-space Laplacian). In particular, such an extension yields results for variable coefficient Schrodinger operators on bounded Lipschitz domains"-- Provided by publisherPPN: PPN: 1922497932
Holdings
Item type Home library Shelving location Call number Status
Institutsbestand Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 57 c-307.2025,1550 Nicht ausleihbar
Total holds: 0
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