Extremal Functions of the Singular Moser-Trudinger Inequality Involving the Eigenvalue

Extremal Functions of the Singular Moser-Trudinger Inequality Involving the Eigenvalue

Year:    2018

Author:    Changliang Zhou, Chunqin Zhou

Journal of Partial Differential Equations, Vol. 31 (2018), Iss. 1 : pp. 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].

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.v31.n1.6

Journal of Partial Differential Equations, Vol. 31 (2018), Iss. 1 : pp. 71–96

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    Singular Moser-Trudinger inequlaity

Author Details

Changliang Zhou

Chunqin Zhou

  1. Compactness of Extremals for Trudinger-Moser Functionals on the Unit Ball in ℝ2

    Shan, Wei Wei | Li, Xiao Meng

    Acta Mathematica Sinica, English Series, Vol. 40 (2024), Iss. 11 P.2840

    https://doi.org/10.1007/s10114-024-3046-9 [Citations: 0]
  2. Extremal Sections for a Trudinger–Moser Functional on Vector Bundle over a Closed Riemann Surface

    Yang, Jie | Yang, Yunyan

    The Journal of Geometric Analysis, Vol. 34 (2024), Iss. 2

    https://doi.org/10.1007/s12220-023-01487-4 [Citations: 2]
  3. Extremal Functions for Trudinger–Moser Inequalities Involving Various $L^{p}$-norms in High Dimension

    Zhao, Juan

    Taiwanese Journal of Mathematics, Vol. 28 (2024), Iss. 4

    https://doi.org/10.11650/tjm/240401 [Citations: 0]