@Article{JPDE-31-71, author = {Zhou , Changliang and Zhou , Chunqin}, title = {Extremal Functions of the Singular Moser-Trudinger Inequality Involving the Eigenvalue}, journal = {Journal of Partial Differential Equations}, year = {2018}, volume = {31}, number = {1}, pages = {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].

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v31.n1.6}, url = {http://global-sci.org/intro/article_detail/jpde/12512.html} }