In this paper, we derive the singular Moser-Trudinger inequality which in-volves the first eigenvalue and several singular points, and further prove the existenceof the extremal functions for the relative Moser-Trudin...In this paper, we derive the singular Moser-Trudinger inequality which in-volves the first eigenvalue and several singular points, and further prove the existenceof the extremal functions for the relative Moser-Trudinger functional. Since the prob-lems involve more complicated norm and multiple singular points, not only we can'tuse the symmetrization to deal with a one-dimensional inequality, but also the pro-cesses of the blow-up analysis become more delicate. In particular, the new inequalityis more general than that of [1, 2].展开更多
文摘In this paper, we derive the singular Moser-Trudinger inequality which in-volves the first eigenvalue and several singular points, and further prove the existenceof the extremal functions for the relative Moser-Trudinger functional. Since the prob-lems involve more complicated norm and multiple singular points, not only we can'tuse the symmetrization to deal with a one-dimensional inequality, but also the pro-cesses of the blow-up analysis become more delicate. In particular, the new inequalityis more general than that of [1, 2].