论文标题
与共形log Sobolev不等式有关的方程解决方案的分类
Classification of solutions of an equation related to a conformal log Sobolev inequality
论文作者
论文摘要
我们对方程式的所有有限能解决方案进行了分类，该方程将作为欧拉（Euler） - 拉格朗日方程式，这是由于贝克纳（Beckner）在球体上不平等不平等的不变的对数sobolev不平等。我们的证明使用了将球体从$ \ mathbb r^n $移动到$ \ mathbb s^n $的方法的扩展，以及Li和Zhu的分类结果。在此过程中，我们证明了与对数拉普拉斯（Googarithmic Laplacian）密切相关的基础操作员的最大最大原理和强大的最大原理。
We classify all finite energy solutions of an equation which arises as the Euler--Lagrange equation of a conformally invariant logarithmic Sobolev inequality on the sphere due to Beckner. Our proof uses an extension of the method of moving spheres from $\mathbb R^n$ to $\mathbb S^n$ and a classification result of Li and Zhu. Along the way we prove a small volume maximum principle and a strong maximum principle for the underlying operator which is closely related to the logarithmic Laplacian.
