Abstract
Let \( \Omega \subset {S^{n - 1}} \) with a smooth boundary \( \partial \Omega \) be the intersection of the cone C with the unit sphere \( {S^{n - 1}}.{\text{Let }}\overrightarrow v \) be the exterior normal to ∂C at points of \( \partial \Omega \) and \( \overrightarrow \tau \) be the exterior with respect to Ω+ normal to σ0 (lying in the tangent to Ω plane). Let γ(ω) be a positive bounded piecewise smooth function on \( \partial \Omega \) and σ(ω) be a positive continuous function on σ0. We consider the eigenvalue problem for the m-Laplace-Beltrami operator on the unit sphere:
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© 2010 Springer Basel AG
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Borsuk, M. (2010). Eigenvalue problem and integro-differential inequalities. In: Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains. Frontiers in Mathematics. Springer, Basel. https://doi.org/10.1007/978-3-0346-0477-2_3
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DOI: https://doi.org/10.1007/978-3-0346-0477-2_3
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Publisher Name: Springer, Basel
Print ISBN: 978-3-0346-0476-5
Online ISBN: 978-3-0346-0477-2
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