{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:32:18Z","timestamp":1777447938666,"version":"3.51.4"},"reference-count":13,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2018,12,6]],"date-time":"2018-12-06T00:00:00Z","timestamp":1544054400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2018,12,6]]},"abstract":"<jats:p>For several different boundary conditions (Dirichlet, Neumann, Robin), we prove norm-resolvent convergence for the operator [Formula: see text] in the perforated domain [Formula: see text], [Formula: see text], to the limit operator [Formula: see text] on [Formula: see text], where [Formula: see text] is a constant depending on the choice of boundary conditions.<\/jats:p>\n                  <jats:p>This is an improvement of previous results [ Progress in Nonlinear Differential Equations and Their Applications 31 ( 1997 ), 45\u201393; in: Proc. Japan Acad., 1985 ], which show strong resolvent convergence. In particular, our result implies Hausdorff convergence of the spectrum of the resolvent for the perforated domain problem.<\/jats:p>","DOI":"10.3233\/asy-181481","type":"journal-article","created":{"date-parts":[[2018,11,13]],"date-time":"2018-11-13T15:50:01Z","timestamp":1542124201000},"page":"163-184","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Norm-resolvent convergence in perforated domains"],"prefix":"10.1177","volume":"110","author":[{"given":"K.","family":"Cherednichenko","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK. E-mail:\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Dondl","sequence":"additional","affiliation":[{"name":"Abteilung f\u00fcr Angewandte Mathematik, Albert-Ludwigs-Universit\u00e4t Freiburg, Hermann-Herder-Stra\u00dfe 10, 79104 Freiburg i. Br., Germany. E-mails:\u00a0,\u00a0"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"R\u00f6sler","sequence":"additional","affiliation":[{"name":"Abteilung f\u00fcr Angewandte Mathematik, Albert-Ludwigs-Universit\u00e4t Freiburg, Hermann-Herder-Stra\u00dfe 10, 79104 Freiburg i. Br., Germany. 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