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].

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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