On principal frequencies and inradius in convex sets
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 Poincaré-Sobolev embedding constants. Eventually, we highlight an open problem.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2018
- DOI:
- 10.48550/arXiv.1808.09684
- arXiv:
- arXiv:1808.09684
- Bibcode:
- 2018arXiv180809684B
- Keywords:
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- Mathematics - Optimization and Control;
- Mathematics - Analysis of PDEs;
- 35P15;
- 49J40;
- 35J70
- E-Print:
- 20 pages, 3 figures