{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:55:13Z","timestamp":1777449313209,"version":"3.51.4"},"reference-count":24,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2016,3,9]],"date-time":"2016-03-09T00:00:00Z","timestamp":1457481600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2016,3,9]]},"abstract":"<jats:p>Let [Formula: see text] be a [Formula: see text]-smooth relatively compact orientable surface with a sufficiently regular boundary. For [Formula: see text], let [Formula: see text] denote the jth negative eigenvalue of the operator associated with the quadratic form [Formula: see text] where \u03c3 is the two-dimensional Hausdorff measure on S. We show that for each fixed j one has the asymptotic expansion [Formula: see text] where [Formula: see text] is the jth eigenvalue of the operator [Formula: see text] on [Formula: see text], in which K and M are the Gauss and mean curvatures, respectively, and [Formula: see text] is the Laplace\u2013Beltrami operator with the Dirichlet condition at the boundary of S. If, in addition, the boundary of S is [Formula: see text]-smooth, then the remainder estimate can be improved to [Formula: see text].<\/jats:p>","DOI":"10.3233\/asy-151341","type":"journal-article","created":{"date-parts":[[2016,3,11]],"date-time":"2016-03-11T09:16:27Z","timestamp":1457687787000},"page":"1-25","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["On eigenvalue asymptotics for strong\n                    <i>\u03b4<\/i>\n                    -interactions supported by surfaces with boundaries"],"prefix":"10.1177","volume":"97","author":[{"given":"Jaroslav","family":"Dittrich","sequence":"first","affiliation":[{"name":"Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, \u0158e\u017e near Prague, Czechia"},{"name":"Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Prague, Czechia. E-mails:\u00a0,\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pavel","family":"Exner","sequence":"additional","affiliation":[{"name":"Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, \u0158e\u017e near Prague, Czechia"},{"name":"Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Prague, Czechia. E-mails:\u00a0,\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"K\u00fchn","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Numerische Mathematik, Technische Universit\u00e4t Graz, Graz, Austria. E-mail:\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Konstantin","family":"Pankrashkin","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques d\u2019Orsay, Univ. Paris-Sud, CNRS, Universit\u00e9 Paris-Saclay, Orsay, France. E-mail:\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2016,3,9]]},"reference":[{"key":"ref001","doi-asserted-by":"publisher","DOI":"10.1090\/chel\/350"},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1142\/S0129055X14500159"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-012-0189-5"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/186"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2004.06.007"},{"key":"ref006","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1994.1188"},{"key":"ref007","doi-asserted-by":"publisher","DOI":"10.3233\/ASY-2002-476"},{"key":"ref008","doi-asserted-by":"publisher","DOI":"10.1007\/PL00005582"},{"key":"ref009","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/339\/06097"},{"key":"ref010","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/077\/2459890"},{"key":"ref011","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/34\/7\/315"},{"key":"ref012","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2014.06.017"},{"key":"ref013","doi-asserted-by":"publisher","DOI":"10.1142\/S0129055X04002084"},{"key":"ref014","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2013.851213"},{"key":"ref015","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-001-8605-2"},{"key":"ref016","doi-asserted-by":"publisher","DOI":"10.1016\/S0393-0440(01)00071-7"},{"key":"ref017","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-010-9681-6"},{"key":"ref018","unstructured":"[18]T.\u00a0Kato, Perturbation Theory for Linear Operators, 2nd edn, Die Grundlehren der mathematischen Wissenschaften, Vol.\u00a0132, Springer, Berlin, Heidelberg, New York, 1980 (corrected printing)."},{"key":"ref019","doi-asserted-by":"publisher","DOI":"10.1088\/0959-7174\/14\/1\/014"},{"key":"ref020","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-18182-0_10"},{"key":"ref021","unstructured":"[21]A.\u00a0Mantile, A.\u00a0Posilicano and M.\u00a0Sini, Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces, available at: arXiv:1505.07236."},{"key":"ref022","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(78)90094-0"},{"key":"ref023","doi-asserted-by":"publisher","DOI":"10.1007\/BF01682875"},{"key":"ref024","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-12040"}],"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-151341","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/ASY-151341","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-151341","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:44Z","timestamp":1777380044000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-151341"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,9]]},"references-count":24,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2016,3,9]]}},"alternative-id":["10.3233\/ASY-151341"],"URL":"https:\/\/doi.org\/10.3233\/asy-151341","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,9]]}}}