0000000000264234
AUTHOR
Paolo Luzzini
Dependence of the layer heat potentials upon support perturbations
We prove that the integral operators associated with the layer heat potentials depend smoothly upon a parametrization of the support of integration. The analysis is carried out in the optimal H\"older setting.
Multi-parameter analysis of the obstacle scattering problem
Abstract We consider the acoustic field scattered by a bounded impenetrable obstacle and we study its dependence upon a certain set of parameters. As usual, the problem is modeled by an exterior Dirichlet problem for the Helmholtz equation Δu + k 2 u = 0. We show that the solution u and its far field pattern u ∞ depend real analytically on the shape of the obstacle, the wave number k, and the Dirichlet datum. We also prove a similar result for the corresponding Dirichlet-to-Neumann map.