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Volume 31, Issue 1
Extremal Functions of the Singular Moser-Trudinger Inequality Involving the Eigenvalue

Changliang Zhou & Chunqin Zhou

DOI: 10.4208/jpde.v31.n1.6

J. Part. Diff. Eq., 31 (2018), pp. 71-96.

Published online: 2018-07

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  • Abstract

In this paper, we derive the singular Moser-Trudinger inequality which involves the first eigenvalue and several singular points, and further prove the existence of the extremal functions for the relative Moser-Trudinger functional. Since the problems involve more complicated norm and multiple singular points, not only we can’t use the symmetrization to deal with a one-dimensional inequality, but also the processes of the blow-up analysis become more delicate. In particular, the new inequality is more general than that of [1, 2].

  • Keywords

Singular Moser-Trudinger inequlaity existence of extremal functions blow up analysis.

  • AMS Subject Headings

46E35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhzhl800130@sjtu.edu.cn (Changliang Zhou)

cqzhou@sjtu.edu.cn (Chunqin Zhou)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-31-71, author = {Zhou , Changliang and Zhou , Chunqin}, title = {Extremal Functions of the Singular Moser-Trudinger Inequality Involving the Eigenvalue}, journal = {Journal of Partial Differential Equations}, year = {2018}, volume = {31}, number = {1}, pages = {71--96}, abstract = {

In this paper, we derive the singular Moser-Trudinger inequality which involves the first eigenvalue and several singular points, and further prove the existence of the extremal functions for the relative Moser-Trudinger functional. Since the problems involve more complicated norm and multiple singular points, not only we can’t use the symmetrization to deal with a one-dimensional inequality, but also the processes of the blow-up analysis become more delicate. In particular, the new inequality is more general than that of [1, 2].

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n1.6}, url = {http://global-sci.org/intro/article_detail/jpde/12512.html} }
TY - JOUR T1 - Extremal Functions of the Singular Moser-Trudinger Inequality Involving the Eigenvalue AU - Zhou , Changliang AU - Zhou , Chunqin JO - Journal of Partial Differential Equations VL - 1 SP - 71 EP - 96 PY - 2018 DA - 2018/07 SN - 31 DO - http://doi.org/10.4208/jpde.v31.n1.6 UR - https://global-sci.org/intro/article_detail/jpde/12512.html KW - Singular Moser-Trudinger inequlaity KW - existence of extremal functions KW - blow up analysis. AB -

In this paper, we derive the singular Moser-Trudinger inequality which involves the first eigenvalue and several singular points, and further prove the existence of the extremal functions for the relative Moser-Trudinger functional. Since the problems involve more complicated norm and multiple singular points, not only we can’t use the symmetrization to deal with a one-dimensional inequality, but also the processes of the blow-up analysis become more delicate. In particular, the new inequality is more general than that of [1, 2].

Zhou , Changliang and Zhou , Chunqin. (2018). Extremal Functions of the Singular Moser-Trudinger Inequality Involving the Eigenvalue. Journal of Partial Differential Equations. 31 (1). 71-96. doi:10.4208/jpde.v31.n1.6
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