On principal frequencies and isoperimetric ratios in convex sets
2020
On a convex set, we prove that the Poincar\'e-Sobolev constant for functions vanishing at the boundary can be bounded from above by the ratio between the perimeter and a suitable power of the $N-$dimensional measure. This generalizes an old result by P\'olya. As a consequence, we obtain the sharp {\it Buser's inequality} (or reverse Cheeger inequality) for the $p-$Laplacian on convex sets. This is valid in every dimension and for every $1
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
16
References
8
Citations
NaN
KQI