Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Fractional Calculus and Applied Analysis, Vol. 8, No 3, (2005), 277p-298p
Abstract:
In this paper, we consider the variations of eigenvalues and eigenfunctions
for the Laplace operator with homogeneous Dirichlet boundary conditions
under deformation of the underlying domain of definition. We derive
recursive formulas for the Taylor coefficients of the eigenvalues as functions
of the shape-perturbation parameter and we establish the existence of a set
of eigenfunctions that is jointly holomorphic in the spatial and boundary-variation
variables. Using integral equations, we show that these eigenvalues
are exactly built with the characteristic values of some meromorphic
operator-valued functions.
