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arXiv · 2112.13371

Principal frequencies of free non-homogeneous membranes and Sobolev extension operators

Vladimir Gol'dshtein·Valerii Pchelintsev·Alexander Ukhlov
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Abstract

Using the quasiconformal mappings theory and Sobolev extension operators, we obtain estimates of principal frequencies of free non-homogeneous membranes. The suggested approach is based on connections between divergence form elliptic operators and quasiconformal mappings. Free non-homogeneous membranes we consider as circular membranes in the quasiconformal geometry associated with non-homogeneity of membranes. As a consequence we get a connection between principal frequencies of free membranes and the smallest-circle problem (initially suggested by J.~J. Sylvester in 1857).

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Vladimir Gol'dshtein, Valerii Pchelintsev, Alexander Ukhlov. 2021-12-26. Principal frequencies of free non-homogeneous membranes and Sobolev extension operators. https://arxiv.org/abs/2112.13371

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