, Volume 3, Issue 2, pp 131-192

Vector Potential Theory on Nonsmooth Domains in R3 and Applications to Electromagnetic Scattering

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We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding theory for Lp-integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering.