Abstract
We extremize the eigenvalues of the Laplacian subject to Dirichlet boundary conditions over starlike planar sets of bounded perimeter and prescribed area. Existence of such extremizers follows from Caratheodory’s notion of set convergence while the necessary conditions are obtained via a marriage of Kato’s perturbation theory and Clarke’s nonsmooth calculus. This necessary condition implies that where the boundary of the extremizer possesses a Holder continuous second derivative it is in fact infinitely differentiable.
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© 1993 Springer Science+Business Media Dordrecht
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Cox, S., Ross, M. (1993). Extremal Eigenvalue Problems for Starlike Drums. In: Bendsøe, M.P., Soares, C.A.M. (eds) Topology Design of Structures. NATO ASI Series, vol 227. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1804-0_25
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DOI: https://doi.org/10.1007/978-94-011-1804-0_25
Publisher Name: Springer, Dordrecht
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