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 - <p>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].</p>