On fractional Poincaré inequalities

Abstract

We show that fractional (p,p)-Poincaré inequalities and even fractional Sobolev-Poincaré inequalities hold for bounded John domains, and especially for bounded Lipschitz domains. We also prove sharp fractional (1,p)-Poincaré inequalities for s-John domains.

Cited by in corpus (2)

• Optimal control of nonlinear systems governed by Dirichlet fractional Laplacian in the minimax framework
• Fractional Hardy-type inequalities in domains with plump complement