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Volume 37, Issue 3
The Compactness of Extremals for a Singular Hardy-Trudinger-Moser Inequality

Qianjin Luo & Xiaomeng Li

DOI: 10.4208/jpde.v37.n3.1

J. Part. Diff. Eq., 37 (2024), pp. 235-250.

Published online: 2024-08

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  • Abstract

Motivated by a recent work of Wang-Yang [19] , we study the compactness of extremals $\{u_β\}$ for singular Hardy-Trudinger-Moser inequalities due to Hou [24] . In particular, by the method of blow-up analysis, we conclude that, up to a subsequence, $u_β$ converges to an extremal in some sense as $β$ tends to zero.

  • Keywords

Compactness, Hardy-Trudinger-Moser inequality, blow-up analysis.

  • AMS Subject Headings

35A01, 35B33, 35B44, 30H10

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JPDE-37-235, author = {Luo , Qianjin and Li , Xiaomeng}, title = {The Compactness of Extremals for a Singular Hardy-Trudinger-Moser Inequality}, journal = {Journal of Partial Differential Equations}, year = {2024}, volume = {37}, number = {3}, pages = {235--250}, abstract = {

Motivated by a recent work of Wang-Yang [19] , we study the compactness of extremals $\{u_β\}$ for singular Hardy-Trudinger-Moser inequalities due to Hou [24] . In particular, by the method of blow-up analysis, we conclude that, up to a subsequence, $u_β$ converges to an extremal in some sense as $β$ tends to zero.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v37.n3.1}, url = {http://global-sci.org/intro/article_detail/jpde/23377.html} }
TY - JOUR T1 - The Compactness of Extremals for a Singular Hardy-Trudinger-Moser Inequality AU - Luo , Qianjin AU - Li , Xiaomeng JO - Journal of Partial Differential Equations VL - 3 SP - 235 EP - 250 PY - 2024 DA - 2024/08 SN - 37 DO - http://doi.org/10.4208/jpde.v37.n3.1 UR - https://global-sci.org/intro/article_detail/jpde/23377.html KW - Compactness, Hardy-Trudinger-Moser inequality, blow-up analysis. AB -

Motivated by a recent work of Wang-Yang [19] , we study the compactness of extremals $\{u_β\}$ for singular Hardy-Trudinger-Moser inequalities due to Hou [24] . In particular, by the method of blow-up analysis, we conclude that, up to a subsequence, $u_β$ converges to an extremal in some sense as $β$ tends to zero.

Qianjin Luo & Xiaomeng Li. (2024). The Compactness of Extremals for a Singular Hardy-Trudinger-Moser Inequality. Journal of Partial Differential Equations. 37 (3). 235-250. doi:10.4208/jpde.v37.n3.1
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