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math.FA2024
A simple proof of attainability for the Sobolev inequality
Megumi Sano
We give a simple proof of the existence of a minimizer for the Sobolev inequality. Our proof is based on a representation formula via a cut-off fundamental solution.
math.FA2022
On the compactness of the (non)radial Sobolev spaces
Shuji Machihara, Megumi Sano
In this note, we give the affirmative answer of the question in [18], which is a compactness result of the non-radial Sobolev spaces. As an application, we show the existence of an…
math.FA2019★ 3 cited
Two limits on Hardy and Sobolev inequalities
Megumi Sano
It is known that classical Hardy and Sobolev inequalities hold when the exponent and the dimension satisfy . In this note, we consider two limits of Hardy a…