论文标题
通过等轴测组的轨道膨胀在非紧密歧管上的紧凑型Sobolev嵌入
Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups
论文作者
论文摘要
鉴于具有一定曲率限制的完整的非紧密riemannian歧管$（m，g）$，我们引入了有关$ g $ $ g $ $ g $ $（m，g）$的扩展条件，该$ g $ $ g $（m，g）在Skrzypczak和Tintarev（Arch。Math。，2013年）中的$ g $的强制性。此外，在这些条件下，证明了sobolev型的嵌入 - berestycki-lions被证明是全范围可允许的参数（Sobolev，Moser-Trudinger和Morrey）。我们还考虑了具有有限的可逆性常数的非紧凑型兰德斯型Finsler歧管的情况，其固定属性与Riemannian同伴相似；这种结构的清晰度通过放克模型显示。作为应用程序，通过使用上述紧凑的嵌入和变分参数来研究兰德斯空间上的quasilinear PDE。
Given a complete non-compact Riemannian manifold $(M,g)$ with certain curvature restrictions, we introduce an expansion condition concerning a group of isometries $G$ of $(M,g)$ that characterizes the coerciveness of $G$ in the sense of Skrzypczak and Tintarev (Arch. Math., 2013). Furthermore, under these conditions, compact Sobolev-type embeddings à la Berestycki-Lions are proved for the full range of admissible parameters (Sobolev, Moser-Trudinger and Morrey). We also consider the case of non-compact Randers-type Finsler manifolds with finite reversibility constant inheriting similar embedding properties as their Riemannian companions; sharpness of such constructions are shown by means of the Funk model. As an application, a quasilinear PDE on Randers spaces is studied by using the above compact embeddings and variational arguments.
