TY - JOUR
T1 - A Singular Moser-Trudinger Inequality on Metric Measure Space
AU - Gui , Yaoting
JO - Journal of Partial Differential Equations
VL - 4
SP - 331
EP - 343
PY - 2022
DA - 2022/10
SN - 35
DO - http://doi.org/10.4208/jpde.v35.n4.3
UR - https://global-sci.org/intro/article_detail/jpde/21052.html
KW - Metric measure space, singular Moser-Trudinger inequality, Ahlfors regularity.
AB - <p style="text-align: justify;">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, \;\; \&nbsp; r&gt;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.</p>