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Bounds and extremal domains for Robin eigenvalues with negative boundary parameter
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SYSNO ASEP 0479662 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Bounds and extremal domains for Robin eigenvalues with negative boundary parameter Author(s) Antunes, P. R. S. (PT)
Freitas, P. (PT)
Krejčiřík, David (UJF-V) RIDNumber of authors 3 Source Title Advances in Calculus of Variations - ISSN 1864-8258
Roč. 10, č. 4 (2017), s. 357-379Number of pages 23 s. Publication form Print - P Language eng - English Country DE - Germany Keywords Eigenvalue optimisation ; Robin Laplacian ; negative boundary parameter ; Bareket's conjecture Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GA14-06818S GA ČR - Czech Science Foundation (CSF) Institutional support UJF-V - RVO:61389005 UT WOS 000411800200003 EID SCOPUS 85030701011 DOI 10.1515/acv-2015-0045 Annotation We present some new bounds for the first Robin eigenvalue with a negative boundary parameter. These include the constant volume problem, where the bounds are based on the shrinking coordinate method, and a proof that in the fixed perimeter case the disk maximises the first eigenvalue for all values of the parameter. This is in contrast with what happens in the constant area problem, where the disk is the maximiser only for small values of the boundary parameter. We also present sharp upper and lower bounds for the first eigenvalue of the ball and spherical shells. These results are complemented by the numerical optimisation of the first four and two eigenvalues in two and three dimensions, respectively, and an evaluation of the quality of the upper bounds obtained. We also study the bifurcations from the ball as the boundary parameter becomes large (negative). Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2018
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