论文标题
关于通过测量保留准文化映射产生的p-Laplacian的Neumann特征值的变化
On Variations of Neumann Eigenvalues of p-Laplacian Generated by Measure Preserving Quasiconformal Mappings
论文作者
论文摘要
在本文中，我们研究了二维$ p $ laplace运算符的第一个非平凡特征值的变化，$ p> 2 $，是通过测量保留准式形式映射$φ的$ \ mathbb d \ toω$，$ω\ subset \ subset \ mathbb r r^2 $产生的。这项研究基于在Sobolev空间上具有尖锐嵌入定理的作用的组成算子的几何理论。通过使用锋利的反向Hölder不平等的版本，我们获得了AHLFORS类型域的第一个非平凡特征值的较低估计。
In this paper we study variations of the first non-trivial eigenvalues of the two-dimensional $p$-Laplace operator, $p>2$, generated by measure preserving quasiconformal mappings $φ: \mathbb D\toΩ$, $Ω\subset\mathbb R^2$. This study is based on the geometric theory of composition operators on Sobolev spaces with applications to sharp embedding theorems. By using a sharp version of the reverse Hölder inequality we obtain lower estimates of the first non-trivial eigenvalues for Ahlfors type domains.
