Ammann, Bernd and Carvalho, Catarina and Nistor, Victor (2012) Regularity for Eigenfunctions of Schrodinger Operators. LETTERS IN MATHEMATICAL PHYSICS, 101 (1). pp. 49-84. ISSN 0377-9017, 1573-0530
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We prove a regularity result in weighted Sobolev (or Babuka-Kondratiev) spaces for the eigenfunctions of certain Schrodinger-type operators. Our results apply, in particular, to a non-relativistic Schrodinger operator of an N-electron atom in the fixed nucleus approximation. More precisely, let be the weighted Sobolev space obtained by blowing up the set of singular points of the potential , , . If satisfies in distribution sense, then for all and all a a parts per thousand currency sign 0. Our result extends to the case when b (j) and c (ij) are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a < 3/2.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | POLYHEDRAL DOMAINS; PSEUDODIFFERENTIAL-OPERATORS; DIFFERENTIAL-OPERATORS; ASYMPTOTIC-BEHAVIOR; SOBOLEV SPACES; WAVE-FUNCTIONS; MANIFOLDS; APPROXIMATION; SINGULARITIES; EQUATION; Hamiltonian; Schrodinger operator; eigenvalues; bound states; regularity of eigenfunctions; blow-up of singularites; singular potentials; multi-electron atoms |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 11 May 2020 08:33 |
| Last Modified: | 11 May 2020 08:33 |
| URI: | https://pred.uni-regensburg.de/id/eprint/18539 |
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