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Surface gradients and continuity properties for some integral operators in classical scattering theory
Author(s) -
Kirsch A.,
Hsiao G. C.
Publication year - 1989
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670110605
Subject(s) - mathematics , sobolev space , helmholtz equation , mathematical proof , mathematical analysis , boundary (topology) , helmholtz free energy , fourier integral operator , boundary value problem , surface (topology) , operator theory , scattering , geometry , physics , quantum mechanics , optics
The surface gradients of some of the most important boundary integral operators for the time‐harmonic Helmholtz and Maxwell equations are computed. These results are used to give new and elementary proofs of the continuity properties of these boundary operators in Sobolev and Hölder spaces of arbitrary order.