An improved Trudinger–Moser inequality and its extremal functions involvingLp-norm inR2
Sign Up to like & getrecommendations! Published in 2020 at "Turkish Journal of Mathematics"
DOI: 10.3906/mat-1907-24
Abstract: Let $W^{1,2} \mathbb{R}^2 $ be the standard Sobolev space. Denote for any real number $p>2$ \begin{align*}\lambda_{p}=\inf\limits_{u\in W^{1,2} \mathbb{R}^2 ,u\not\equiv0}\frac{\int_{\mathbb{R}^{2}} |\nabla u|^2+|u|^2 dx}{ \int_{\mathbb{R}^{2}}|u|^pdx ^{2/p}}. \end{align*} Define a norm in $W^{1,2} \mathbb{R}^2 $ by \begin{align*}\|u\|_{\alpha,p}=\left \int_{\mathbb{R}^{2}}… read more here.
Keywords: moser inequality; trudinger moser; int mathbb; mathbb ... See more keywords