Data di Pubblicazione:
2009
Citazione:
Best constants for Moser type inequalities in Zygmund spaces / D. Cassani, B. Ruf, C. Tarsi. - In: MATEMATICA CONTEMPORANEA. - ISSN 0103-9059. - 36:(2009), pp. 79-90.
Abstract:
We first survey some recent results on optimal embeddings for the
space of functions whose \Delta u\in L^1(\Omega), where
\Omega\subsetR^2 is a bounded domain. The target space in the
embeddings turns out to be a Zygmund space and the best
constants are explicitly known. Remarkably, the best constant in
the case of zero boundary data is twice the best constant in the
case of compactly supported functions. Then, following the same
strategy, we establish a new version of the celebrated
Trudinger--Moser inequality, in the Zygmund space
Z_0^{1/2}(\Omega), and we prove that, in contrast to the Moser
case, here the best embedding constant is not attained.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
D. Cassani, B. Ruf, C. Tarsi
Link alla scheda completa: