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].