Sobolev inequalities with jointly concave weights on convex cones

Zoltán M. Balogh, Cristian E. Gutiérrez, Alexandru Kristály

Using optimal mass transport arguments, we prove weighted Sobolev inequalities of the form \[\left(\int_E |u(x)|^q\,ω(x) \,dx\right)^{1/q}\leq K_0\,\left(\int_E |\nabla u(x)|^p\,σ(…