Volume 26, Issue 4
A New Proof of Subcritical Trudinger-Moser Inequalities on the Whole Euclidean Space

J. Part. Diff. Eq., 26 (2013), pp. 300-304.

Published online: 2013-12

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• Abstract

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

• Keywords

46E30

yunyanyang@ruc.edu.cn (Yunyan Yang)

zhuxiaobao@ruc.edu.cn (Xiaobao Zhu)

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@Article{JPDE-26-300, author = {Yang , Yunyan and Zhu , Xiaobao}, title = {A New Proof of Subcritical Trudinger-Moser Inequalities on the Whole Euclidean Space}, journal = {Journal of Partial Differential Equations}, year = {2013}, volume = {26}, number = {4}, pages = {300--304}, abstract = {

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

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v26.n4.2}, url = {http://global-sci.org/intro/article_detail/jpde/5166.html} }
TY - JOUR T1 - A New Proof of Subcritical Trudinger-Moser Inequalities on the Whole Euclidean Space AU - Yang , Yunyan AU - Zhu , Xiaobao JO - Journal of Partial Differential Equations VL - 4 SP - 300 EP - 304 PY - 2013 DA - 2013/12 SN - 26 DO - http://doi.org/10.4208/jpde.v26.n4.2 UR - https://global-sci.org/intro/article_detail/jpde/5166.html KW - Trudinger-Moser inequality KW - Adams inequality AB -

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

Yunyan Yang & Xiaobao Zhu. (2019). A New Proof of Subcritical Trudinger-Moser Inequalities on the Whole Euclidean Space. Journal of Partial Differential Equations. 26 (4). 300-304. doi:10.4208/jpde.v26.n4.2
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