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

作者：Cassani Daniele^*; Tarsi Cristina

来源：Asymptotic Analysis, 2009, 64(1-2): 29-51.

DOI：10.3233/ASY-2009-0934

• Lorentz-Sobolev spaces
• limiting Sobolev embeddings
• Trudinger-Moser type inequalities
• unbounded domains
• best constants

We derive a Pohozaev-Trudinger type embedding for the Lorentz-Sobolev space (W0LN,q)-L-1(Omega), for general domains Omega subset of R-N and in particular for Omega = 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.