On principal frequencies and inradius in convex sets

Lorenzo Brasco

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arXiv · 1808.09684

On principal frequencies and inradius in convex sets

Lorenzo Brasco

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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 Poincar\'e-Sobolev embedding constants. Eventually, we highlight an open problem.

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Lorenzo Brasco. 2018-08-29. On principal frequencies and inradius in convex sets. https://arxiv.org/abs/1808.09684

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