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Math."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical study of the extremal domains for the first eigenvalue, from which we see that these depend on the value of the compression, and start developing a boundary structure as this parameter is increased. The corresponding number of nodal domains of the first eigenfunction of the extremal domain also increases with the compression.<\/jats:p>","DOI":"10.1137\/19m1249606","type":"journal-article","created":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T14:28:51Z","timestamp":1569335331000},"page":"1872-1891","source":"Crossref","is-referenced-by-count":8,"title":["On the Behavior of Clamped Plates under Large Compression"],"prefix":"10.1137","volume":"79","author":[{"given":"P. R. S.","family":"Antunes","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1451-4358","authenticated-orcid":true,"given":"D.","family":"Buoso","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Freitas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,9,24]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2404"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/44\/21\/215205"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/130948860"},{"key":"atypb4","unstructured":"M. S. Ashbaugh, R. Benguria, and R. Mahadevan,\n                      A Sharp Lower Bound for the First Eigenvalue of the Vibrating Clamped Plate Problem under Compression\n                      , preprint, 2018."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-95-07801-6"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144503437336"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"D. Bucur,\n                      Existence results\n                      , in Shape Optimization and Spectral Theory, A. Henrot, ed., De Gruyter Open, Warsaw, Berlin, 2017,https:\/\/doi.org\/10.1515\/9783110550887-002.","DOI":"10.1515\/9783110550887-002"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"D. Bucur, P. Freitas, and J. B. Kennedy,\n                      The Robin problem\n                      , in Shape Optimization and Spectral Theory, A. Henrot, ed., De Gruyter Open, Warsaw, Berlin, 2017,https:\/\/doi.org\/10.1515\/9783110550887-004.","DOI":"10.1515\/9783110550887-004"},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"D. Buoso,\n                      Analyticity and criticality results for the eigenvalues of the biharmonic operator\n                      , in Geometric Properties for Parabolic and Elliptic PDE's, Springer Proc. Math. Stat. 176, Springer, Cham, 2016,https:\/\/doi.org\/10.1007\/978-3-319-41538-3_5.","DOI":"10.1007\/978-3-319-41538-3_5"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2013054"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1080\/00036811.2018.1451639"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.5802\/afst.712"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"M. C. Delfour and J.P. Zol\u00e9sio,\n                      Shapes and Geometries: Analysis, Differential Calculus, and Optimization\n                      , Adv. Des. Control 4, SIAM, Philadelphia, 2001,https:\/\/doi.org\/10.1137\/1.9780898719826.","DOI":"10.1137\/1.9780898719826"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01774296"},{"key":"atypb15","unstructured":"P. Freitas and R. Laugesen,\n                      From Neumann to Steklov and Beyond, via Robin: The Weinberger Way\n                      , preprint,https:\/\/arxiv.org\/abs\/1810.07461, 2018."},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"F. Gazzola, H.C. Grunau, and G. Sweers,\n                      Polyharmonic Boundary Value Problems. Positivity Preserving and Nonlinear Higher Order Elliptic Equations in Bounded Domains\n                      , Lecture Notes in Math. 1991, Springer-Verlag, Berlin, 2010,https:\/\/doi.org\/10.1007\/978-3-642-12245-3.","DOI":"10.1007\/978-3-642-12245-3"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-010-9681-6"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"A. Henrot and M. Pierre,\n                      Variation et optimisation de formes. Une analyse g\u00e9om\u00e9trique\n                      , Math. Appl. (Berlin) 48, Springer, Berlin, 2005,https:\/\/doi.org\/10.1007\/3-540-37689-5.","DOI":"10.1007\/3-540-37689-5"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/0524022"},{"key":"atypb20","unstructured":"M. Kitahara,\n                      Boundary Integral Equation Methods in Eigenvalue Problems of Elastodynamics and Thin Plates\n                      , Elsevier, Amsterdam, 1985."},{"key":"atypb21","unstructured":"A. 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Rayleigh,\n                      The Theory of Sound\n                      , 2nd ed., Dover, New York, 1945."},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1007\/BF00250468"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1249606","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:20:44Z","timestamp":1787340044000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1249606"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":27,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/19M1249606"],"URL":"https:\/\/doi.org\/10.1137\/19m1249606","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}