Generalizations of the Trudinger-Moser inequality to Sobolev-Lorentz spaces with weights are considered. The weights in these spaces allow for the addition of certain lower order terms in the exponential integral. We prove an explicit relation between the weights and the lower order terms; furthermore, we show that the resulting inequalities are sharp, and that there are related phenomena of concentration-compactness.
On Trudinger–Moser type inequalities involving Sobolev–Lorentz spaces / B. Ruf, C. Tarsi. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 188:3(2009 Jul), pp. 369-397. [10.1007/s10231-008-0077-2]
On Trudinger–Moser type inequalities involving Sobolev–Lorentz spaces
B. RufPrimo
;C. TarsiUltimo
2009
Abstract
Generalizations of the Trudinger-Moser inequality to Sobolev-Lorentz spaces with weights are considered. The weights in these spaces allow for the addition of certain lower order terms in the exponential integral. We prove an explicit relation between the weights and the lower order terms; furthermore, we show that the resulting inequalities are sharp, and that there are related phenomena of concentration-compactness.
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