@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} }