论文标题
凸锥中Sobolev不平等的极端和关键点的概述
An overview on extremals and critical points of the Sobolev inequality in convex cones
论文作者
论文摘要
在这项调查中，我们考虑了凸锥中尖锐的Sobolev不平等。我们还使用最佳运输技术证明了这一点。然后，我们提出了一些与Sobolev不平等的Euler-Lagrange方程相关的结果：所谓的临界p-Laplace方程。最后，我们讨论了与Sobolev不平等有关的一些稳定结果。
In this survey, we consider the sharp Sobolev inequality in convex cones. We also prove it by using the optimal transport technique. Then we present some results related to the Euler-Lagrange equation of the Sobolev inequality: the so-called critical p-Laplace equation. Finally, we discuss some stability results related to the Sobolev inequality.
