JournalsjstVol. 10, No. 1pp. 337–353

Sobolev extension operators and Neumann eigenvalues

  • Vladimir Gol'dshtein

    Ben-Gurion University of the Negev, Beer Sheva, Israel

  • Valerii Pchelintsev

    Ben Gurion University of the Negev, Beer-Sheva, Israel; Tomsk Polytechnic University and Tomsk State University, Russia

  • Alexander Ukhlov

    Ben-Gurion University of the Negev, Beer Sheva, Israel
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Abstract

In this paper we apply estimates of the norms of Sobolev extension operators to the spectral estimates of the first non-trivial Neumann eigenvalue of the Laplace operator in non-convex extension domains. As a consequence we obtain a connection between resonant frequencies of free membranes and the smallest-circle problem(initially proposed by J. J. Sylvester in 1857).

Cite this article

Vladimir Gol'dshtein, Valerii Pchelintsev, Alexander Ukhlov, Sobolev extension operators and Neumann eigenvalues. J. Spectr. Theory 10 (2020), no. 1, pp. 337–353

DOI 10.4171/JST/295