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Sharp norm estimates of layer potentials and operators at high frequency

Han, Xiaolong; Tacy, Melissa

Description

In this paper, we investigate single and double layer potentials mapping boundary data to interior functions of a domain at high frequency λ2→∞. In the high frequency regime the key problem is the dependence of mapping norms on the parameter λ. For single layer potentials, we find that the L2(∂Ω)→L2(Ω) norms decay in λ. The rate of decay depends on the curvature of ∂Ω: The norm is λ-3/4 in piecewise smooth domains and λ-5/6 if the boundary ∂Ω is positively curved. The double layer potential,...[Show more]

CollectionsANU Research Publications
Date published: 2015
Type: Journal article
URI: http://hdl.handle.net/1885/98465
Source: Journal of Functional Analysis
DOI: 10.1016/j.jfa.2015.06.011

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