In this paper, suppose [Formula: see text] be a convex function of class [Formula: see text] which is even and positively homogeneous of degree 1. We establish the Lions type concentration-compactness principle of singular Trudinger–Moser Inequalities involving [Formula: see text]-Finsler–Laplacian operator. Let [Formula: see text] be a smooth bounded domain. [Formula: see text] be a sequence such that anisotropic Dirichlet norm[Formula: see text], [Formula: see text] weakly in [Formula: see text]. Denote [Formula: see text] Then we have [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] is the volume of a unit Wulff ball. This conclusion fails if [Formula: see text]. Furthermore, we also obtain the corresponding concentration-compactness principle in the entire Euclidean space [Formula: see text].

中文翻译：

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涉及 N-Finsler-Laplacian 算子的奇异 Trudinger-Moser 不等式的集中紧致原理

在本文中，假设 [公式：见正文] 是类 [公式：见正文] 的凸函数，它是 1 次偶正齐次的。我们建立了奇异 Trudinger-Moser 不等式的 Lions 型集中紧致性原理，涉及 [公式：见正文]-Finsler-Laplacian 算子。让 [公式：见正文] 是一个光滑的有界域。[公式：见文]是一个序列，使得各向异性狄利克雷范数[公式：见文]，[公式：见文]弱于[公式：见文]。表示 [Formula: see text] 然后我们有 [Formula: see text] 其中 [Formula: see text]、[Formula: see text] 和 [Formula: see text] 是单位 Wulff 球的体积。如果 [公式：见正文]，则此结论不成立。此外，我们还得到了整个欧几里得空间中相应的浓度-紧致性原理[公式：见正文]。