On principal frequencies and inradius in convex sets
Brasco, Lorenzo
Bruno Pini Mathematical Analysis Seminar, (2018), / Harvested from Bruno Pini Mathematical Analysis Seminar
Link
Link

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.

Publié le : 2018-01-01
DOI : https://doi.org/10.6092/issn.2240-2829/8945 
@article{8945,
     title = {On principal frequencies and inradius in convex sets},
     journal = {Bruno Pini Mathematical Analysis Seminar},
     year = {2018},
     doi = {10.6092/issn.2240-2829/8945},
     language = {EN},
     url = {http://dml.mathdoc.fr/item/8945}
}

Brasco, Lorenzo. On principal frequencies and inradius in convex sets. Bruno Pini Mathematical Analysis Seminar,  (2018), . doi : 10.6092/issn.2240-2829/8945. http://gdmltest.u-ga.fr/item/8945/