A Moser-type inequality in Lorentz–Sobolev spaces for unbounded domains in R N

Abstract

We derive a Pohožaev–Trudinger type embedding for the Lorentz–Sobolev space W¹₀L^N,q(Ω), for general domains Ω⊆R^N and in particular for Ω=R^N. Precisely, we first prove that the corresponding inequality is domain independent and then, by constructing explicit concentrating sequences à la Moser, we establish that the embedding inequality is sharp and we exhibit the best constant.