Poincaré and Sobolev inequalities with variable exponents and log-Holder continuity only at the boundary

David Cruz-Uribe, Fernando López-García, Ignacio Ojea

We prove Sobolev-Poincaré and Poincaré inequalities in variable Lebesgue spaces $L^{p(\cdot )}(\Omega )$, with $\Omega \subset {\mathbb{R}}^n$ a bounded John domain, with weaker regularity assump…