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

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We study variations of the first nontrivial eigenvalue of the two-dimensional p-Laplace operator, p > 2, generated by measure preserving quasiconformal mappings. The study is based on the geometric theory of composition operators in Sobolev spaces and sharp embedding theorems. Using a sharp version of the reverse Hölder inequality, we obtain a lower estimate for the first nontrivial eigenvalue in the case of Ahlfors type domains.

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Authors and Affiliations

  1. Tomsk Polytechnic University, 30, Lenin Ave., Tomsk, 634050, Russia

    V. A. Pchelintsev

  2. Tomsk State University, 36, Lenin Ave., Tomsk, 634050, Russia

    V. A. Pchelintsev

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  1. V. A. Pchelintsev
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Correspondence to V. A. Pchelintsev.

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Translated from Problemy Matematicheskogo Analiza 108, 2021, pp. 139-147.

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Pchelintsev, V.A. On Variations of the Neumann Eigenvalues of p-Laplacian Generated by Measure Preserving Quasiconformal Mappings. J Math Sci 255, 503–512 (2021). https://doi.org/10.1007/s10958-021-05388-1

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  • DOI: https://doi.org/10.1007/s10958-021-05388-1

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