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Physically, the above problems correspond to the determination of the shapes within a given class which will support the largest number of modes below a given frequency.<\/jats:p>","DOI":"10.1063\/1.4803140","type":"journal-article","created":{"date-parts":[[2013,5,3]],"date-time":"2013-05-03T22:51:33Z","timestamp":1367621493000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":19,"title":["Asymptotic behaviour of optimal spectral planar domains with fixed perimeter"],"prefix":"10.1063","volume":"54","author":[{"given":"Dorin","family":"Bucur","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Savoie 1 Laboratoire de Math\u00e9matiques (LAMA), , Campus Scientifique, 73376 Le-Bourget-Du-Lac, France"}]},{"given":"Pedro","family":"Freitas","sequence":"additional","affiliation":[{"name":"Faculdade de Motricidade Humana (TU Lisbon) and Group of Mathematical Physics of the University of Lisbon 2 Department of Mathematics, , Complexo Interdisciplinar, Av. Prof. Gama Pinto 2, P-1649-003 Lisboa, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2013,5,3]]},"reference":[{"key":"2023062717165485600_c1","article-title":"Functions of bounded variation and free discontinuity problems","volume-title":"Oxford Mathematical Monographs","year":"2000"},{"key":"2023062717165485600_c2","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/s10957-011-9983-3","article-title":"Numerical optimisation of low eigenvalues of the Dirichlet and Neumann Laplacians","volume":"154","year":"2012","journal-title":"J. Optim. Theory Appl."},{"key":"2023062717165485600_c3","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2012.0492","article-title":"Optimal spectral rectangles and lattice ellipses","volume":"469","year":"2013","journal-title":"Proc. R. Soc. London, Ser. 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