Sharp norm estimates of layer potentials and operators at high frequency
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|
|Source:||Journal of Functional Analysis|
|01_Han_Sharp_norm_estimates_of_layer_2015.pdf||551.74 kB||Adobe PDF||Request a copy|
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