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arXiv · 2012.07059

On Variations of Neumann Eigenvalues of p-Laplacian Generated by Measure Preserving Quasiconformal Mappings

Valerii Pchelintsev
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Abstract

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 $\varphi : \mathbb D\to\Omega$, $\Omega \subset\mathbb R^2$. 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 H\"older inequality we obtain lower estimates of the first non-trivial eigenvalues for Ahlfors type domains.

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Valerii Pchelintsev. 2020-12-13. On Variations of Neumann Eigenvalues of p-Laplacian Generated by Measure Preserving Quasiconformal Mappings. https://arxiv.org/abs/2012.07059

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