Year: 2022
Author: Yaoting Gui
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 4 : pp. 331–343
Abstract
Let $(X,d,\mu)$ be a metric space with a Borel-measure $\mu$, suppose $\mu$ satisfies the Ahlfors-regular condition, i.e. \begin{equation*} b_1r^s\leq\mu(B_r(x))\leq b_2r^s,\qquad \forall B_r(x)\subset X, \;\; \ r>0, \end{equation*} where $b_1$, $b_2$ are two positive constants and $s$ is the volume growth exponent. In this paper, we mainly study two things, one is to consider the best constant of the Moser-Trudinger inequality on such metric space under the condition that $s$ is not less than 2. The other is to study the generalized Moser-Trudinger inequality with a singular weight.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v35.n4.3
Journal of Partial Differential Equations, Vol. 35 (2022), Iss. 4 : pp. 331–343
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Metric measure space singular Moser-Trudinger inequality Ahlfors regularity.