From affine Poincar\'e inequalities to affine spectral inequalities

11 Jul 2020 Haddad Julián Jiménez Carlos Hugo Montenegro Marcos

Given a bounded open subset $\Omega$ of $\mathbb R^n$, we establish the weak closure of the affine ball $B^{\mathcal A}_p(\Omega) = \{f \in W^{1,p}_0(\Omega):\ \mathcal E_p f \leq 1\}$ with respect to the affine functional $\mathcal E_pf$ introduced by Lutwak, Yang and Zhang in [43] as well as its compactness in $L^p(\Omega)$ for any $p \geq 1$. These points use strongly the celebrated Blaschke-Santal\'{o} inequality... (read more)

PDF Abstract
No code implementations yet. Submit your code now

Categories


  • ANALYSIS OF PDES
  • FUNCTIONAL ANALYSIS
  • METRIC GEOMETRY