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 - <p>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.</p>