Hardy–Sobolev inequalities in the half-space for double phase functionals

Abstract

We establish Hardy–Sobolev inequalities in the half-space for double phase functionals $\mathrm{\Phi }(x,t)$ of the form $t^p+{(b(x)t)}^q$, where , $b(\cdot )$ is nonnegative and Hölder continuous of order $\theta \in (0,1]$.