摘要
The first aim of this article is to study the sharp singular(two-weight)Trudinger-Moser inequalities with Finsler norms on R^(2).The second goal is to propose a different approach to study a vanishing-concentration-compactness principle for the Trudinger-Moser inequalities and use this to investigate the existence and the nonexistence of the maximizers for the Trudinger-Moser inequalities in the subcritical regions.Finally,by applying our Finsler Trudinger-Moser inequalities to suitable Finsler norms,we derive the sharp affine Trudinger-Moser inequalities which are essentially stronger than the Trudinger-Moser inequalities with standard energy of the gradient.
