Data di Pubblicazione:
2024
Citazione:
A log-weighted Moser inequality on the plane / C. Tarsi. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 241:(2024), pp. 113466.1-113466.14. [10.1016/j.na.2023.113466]
Abstract:
We establish a sharp Moser type inequality with logarithmic weight in the nonradial mass-
weighted Sobolev spaces, on the whole plane R2. We identify the sharp threshold for the uniform
boundedness of the weighted Moser functional, which is still given by 4𝜋: further, we prove
the validity of the inequality also at the limiting sharp value 4𝜋. Even if the increasing nature
of the log weight prevents the application of any symmetrization tool, we prove our inequality
in the general framework of Sobolev space, and not on radial subspaces, as in the available
literature. The main strategy is a careful analysis of the behaviour of the normalized maximizing
sequences.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Trudinger-Moser inequalities; weighted Sobolev spaces; concentration-compactness at infinity
Elenco autori:
C. Tarsi
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