Upper bound for the first $p$-Steklov eigenvalue in ${\mathbb{R}}^n$

Lili Wang, Tao Wang

For $p\in (1,n]$ and any bounded convex domain $\Omega \subset {\mathbb{R}}^n$, we prove the sharp inequality \[ Λ_p(Ω):=\frac{W_p(Ω)}{P(Ω)V(Ω)^{p/n}}\geqω_n^{-p/n}, \qquad W_p(Ω)=\int_{\par…