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Volume 35, Issue 4
A Singular Moser-Trudinger Inequality on Metric Measure Space

Yaoting Gui

DOI: 10.4208/jpde.v35.n4.3

J. Part. Diff. Eq., 35 (2022), pp. 331-343.

Published online: 2022-10

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  • 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.

  • Keywords

Metric measure space, singular Moser-Trudinger inequality, Ahlfors regularity.

  • AMS Subject Headings

51F99, 31E05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

vigney@mail.ustc.edu.cn (Yaoting Gui)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-35-331, author = {Gui , Yaoting}, title = {A Singular Moser-Trudinger Inequality on Metric Measure Space}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {35}, number = {4}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v35.n4.3}, url = {http://global-sci.org/intro/article_detail/jpde/21052.html} }
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 -

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.

Gui , Yaoting. (2022). A Singular Moser-Trudinger Inequality on Metric Measure Space. Journal of Partial Differential Equations. 35 (4). 331-343. doi:10.4208/jpde.v35.n4.3
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