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 W 1 0 L 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.