Galkowski, Jeffrey;
Wunsch, Jared;
(2025)
Propagation for Schrodinger operators with potentials singular along a hypersurface.
Archive for Rational Mechanics and Analysis
, 248
, Article 37. 10.1007/s00205-024-01965-1.
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Abstract
In this article, we study propagation of defect measures for Schrödinger operators, −h 2∆g + V , on a Riemannian manifold (M, g) of dimension n with V having conormal singularities along a hypersurface Y in the sense that derivatives along vector fields tangent to Y preserve the regularity of V . We show that the standard propagation theorem holds for bicharacteristics travelling transversally to the surface Y whenever the potential is absolutely continuous. Furthermore, even when bicharacteristics are tangent to Y at exactly first order, as long as the potential has an absolutely continuous first derivative, standard propagation continues to hold.
| Type: | Article |
|---|---|
| Title: | Propagation for Schrodinger operators with potentials singular along a hypersurface |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00205-024-01965-1 |
| Publisher version: | http://doi.org/10.1007/s00205-024-01965-1 |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10186930 |
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