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

Changliang Zhou and Chunqin Zhou

10.4208/jpde.v31.n1.6

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

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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].

  • History

Published online: 2018-07

  • AMS Subject Headings

46E35

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