Sharp norm estimates of layer potentials and operators at high frequency
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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]
Collections | ANU Research Publications |
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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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01_Han_Sharp_norm_estimates_of_layer_2015.pdf | 551.74 kB | Adobe PDF | Request a copy |
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