On principal frequencies and inradius in convex sets

Lorenzo Brasco

Abstract


We generalize to the case of the p-Laplacian an old result by Hersch and Protter. Namely, we show that it is possible to estimate from below the first eigenvalue of the Dirichlet p-Laplacian of a convex set in terms of its inradius. We also prove a lower bound in terms of isoperimetric ratios and we briefly discuss the more general case of Poincarè-Sobolev embedding constants. Eventually, we highlight an open problem.

Keywords


Convex sets; p-Laplacian; nonlinear eigenvalue problems; inradius; Cheeger constant

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DOI: 10.6092/issn.2240-2829/8945

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Copyright (c) 2018 Lorenzo Brasco

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