We derive a Pohoaev-Trudinger type embedding for the Lorentz-Sobolev space W1"0LN,q(Ω), for general domains Ω⊆RN and in particular for Ω=RN. 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.
A Moser-type inequality in Lorentz-Sobolev spaces for unbounded domains in R^N / D. Cassani, C. Tarsi. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 64:1-2(2009), pp. 29-51.
A Moser-type inequality in Lorentz-Sobolev spaces for unbounded domains in R^N
C. TarsiUltimo
2009
Abstract
We derive a Pohoaev-Trudinger type embedding for the Lorentz-Sobolev space W1"0LN,q(Ω), for general domains Ω⊆RN and in particular for Ω=RN. 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.
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