Extremals for a Trudinger-Moser Inequality with a Vanishing Weight in the Unit Disk
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DOI: 10.1007/s10476-020-0049-3
Abstract: In this paper, we study a Trudinger-Moser inequality with a vanishing weight in the unit disk. Precisely, let $$B$$ B be the unit disk and β ≥ 0 be a real number. Denote $${\cal S}… read more here.
Keywords: unit disk; unit; inequality vanishing; moser inequality ... See more keywords
A remark on an improved Trudinger–Moser inequality in high dimensions
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DOI: 10.1080/17476933.2019.1647183
Abstract: ABSTRACT Let be the unit ball in , be the standard Sobolev space. We consider an improved Trudinger–Moser inequality involving -norm. Denote the first eigenvalue of the n-Laplacian operator. We prove that for any p>1… read more here.
Keywords: moser inequality; trudinger moser; inequality; improved trudinger ... See more keywords
An improved Trudinger–Moser inequality and its extremal functions involvingLp-norm inR2
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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