Abstract
Taking various viewpoints, we study the selfadjoint extensions \( \mathcal{A} \) of the operator A of the Dirichlet problem in a 3-dimensional region Ω with an edge Γ. We identify the infinite dimensional nullspace def A with the Sobolev space H −ϰ(Γ) on Γ with variable smoothness exponent −ϰ ∈ (−1, 0); while the selfadjoint extensions, with selfadjoint operators \( \mathcal{T} \) on the subspaces of H −ϰ(Γ). To the boundary value problem in the region with a “smoothed” edge we associate a concrete extension, which yields a more precise approximate solution to the singularly perturbed problem.
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Original Russian Text © S.A. Nazarov, 2008, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2008, Vol. XI, No. 1, pp. 80–95.
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Nazarov, S.A. Selfadjoint extensions of the operator of the Dirichlet problem in a 3-dimensional region with an edge. J. Appl. Ind. Math. 3, 377–390 (2009). https://doi.org/10.1134/S1990478909030089
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DOI: https://doi.org/10.1134/S1990478909030089