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

摘要

We derive a Pohozaev-Trudinger type embedding for the Lorentz-Sobolev space W_0~1L~(N,q)(Ω), for general domains Ω is contained in 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 a la Moser, we establish that the embedding inequality is sharp and we exhibit the best constant.