Spectral theory of Neumann-Poincare operator and applications
Hyeonbae Kang () /
The Neumann-Poincare (NP) operator is a boundary integral operator which arises naturally when solving boundary value problems using layer potentials. It is not self-adjoint with the usual inner product. But it can symmetrized by introducing a new inner product on $H^{-1/2}$ spaces using Plemelj's symmetrization principle. Recently many interesting spectral properties of the NP operator have been discovered. I will discuss about this development and various applications including solvability of PDEs with complex coefficients and plasmonic resonance.