From affine Poincaré inequalities to affine spectral inequalities

Julián Haddad, Carlos Hugo Jiménez, Marcos Montenegro

Given a bounded open subset $\Omega$ of ${\mathbb{R}}^n$, we establish the weak closure of the affine ball $B_p^{\mathcal{A}}(\Omega )=\{f\in W_0^{1,p}(\Omega ):{\mathcal{E}}_{p}f\le 1\}$ with respe…