The spectra of harmonic layer potential operators on domains with rotationally symmetric conical points

摘要: Abstract We study the adjoint of double layer potential associated with Laplacian (the Neumann–Poincare operator), as a map on boundary surface Γ domain in R 3 conical points. The spectrum this operator directly reflects well-posedness related transmission problems across Γ. In particular, if is understood an inclusion complex permittivity ϵ, embedded background medium unit permittivity, then polarizability tensor well-defined when ( ϵ + 1 ) / − belongs to resolvent set energy norm. surfaces that have finite number points featuring rotational symmetry. On space, we show essential consists interval. L 2 , i.e. for square-integrable data, countable union curves, outside which Fredholm index can be computed winding respect spectrum. provide explicit formulas, depending opening angles reinforce our very precise numerical experiments, computing space and spectral measures two different examples. Our results indicate densities may approach zero extremely rapidly continuous part