A DECAY ESTIMATE FOR THE EIGENVALUES OF THE NEUMANN-POINCARE OPERATOR USING THE GRUNSKY COEFFICIENTS

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We consider the decay property of the eigenvalues of the NeumannPoincare operator in two dimensions. As is well known, this operator admits only a sequence of eigenvalues that accumulates to zero as its spectrum for a bounded domain having C-1,C-alpha boundary with alpha is an element of (0, 1). We show that the eigenvalues lambda(k) of the Neumann-Poincare operator ordered by size satisfy that vertical bar lambda(k)vertical bar = O(k(-p-alpha+1/2)) for an arbitrary simply connected domain having C-1+p,C-alpha boundary with p >= 0, alpha is an element of (0,1), and p + alpha > 1/2.
Publisher
AMER MATHEMATICAL SOC
Issue Date
2020-02
Language
English
Article Type
Article
Citation

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.148, no.2, pp.591 - 600

ISSN
0002-9939
DOI
10.1090/proc/14785
URI
http://hdl.handle.net/10203/274173
Appears in Collection
MA-Journal Papers(저널논문)
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