A new proof of subcritical Trudinger-Moser inequalities on the whole Euclidean space

Yunyan Yang; Xiaobao Zhu

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arXiv · 1210.1963

A new proof of subcritical Trudinger-Moser inequalities on the whole Euclidean space

Yunyan Yang·Xiaobao Zhu

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Abstract

In this note, we give a new proof of subcritical Trudinger-Moser inequality on $\mathbb{R}^n$. All the existing proofs on this inequality are based on the rearrangement argument with respect to functions in the Sobolev space $W^{1,n}(\mathbb{R}^n)$. Our method avoids this technique and thus can be used in the Riemannian manifold case and in the entire Heisenberg group.

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Yunyan Yang, Xiaobao Zhu. 2012-10-06. A new proof of subcritical Trudinger-Moser inequalities on the whole Euclidean space. https://arxiv.org/abs/1210.1963

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