2025/04/01 by Riva, Matteo Dalla, Lamberti, Pier Domenico, Luzzini, Paolo +1
#31A10 #31B10 #35B20 #35P99 #47A10 #47A11 #47A55 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2504.00696
This paper concerns the eigenvalues of the Neumann-Poincaré operator, a boundary integral operator associated with the harmonic double-layer potential. Specifically, we examine how the eigenvalues depend on the support of integration and prove that the map associating the support's shape to the eigenvalues is real-analytic. We then compute its first derivative and present applications of the resulting formula. The proposed method allows for handling infinite-dimensional perturbation parameters for multiple eigenvalues and perturbations that are not necessarily in the normal direction.