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On the isoperimetric inequality for the buckling of a clamped plate

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Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Abstract

In two dimensions, we prove the existence of a domain minimizing the buckling load of a clamped plate among all domains of given measure. In order to prove that the optimal set is the disk, we discuss possible ways of applying an idea of Willms and Weinberger if the regularity of the optimal set is not a priori assumed.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, MO 65211, Columbia, USA

    S. Ashbaugh

  2. Département de Mathématiques, Université de Metz, Ile du Saulcy, 57045, Metz Cedex, France

    Dorin Bucur

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  1. S. Ashbaugh
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  2. Dorin Bucur
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Correspondence to S. Ashbaugh.

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Ashbaugh, S., Bucur, D. On the isoperimetric inequality for the buckling of a clamped plate . Z. angew. Math. Phys. 54, 756–770 (2003). https://doi.org/10.1007/s00033-003-3204-3

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  • DOI: https://doi.org/10.1007/s00033-003-3204-3

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