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

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Singular Moser-Trudinger inequlaity existence of extremal functions blow up analysis
• 年，卷（期）: 2018,（1）
• 页码范围: 71-96
• 页数: 26页
• 分类号: O175.25
• 语种: 英文
• DOI: 10.4208/jpde.v31.n1.6

摘要

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 [l,2].