TY - JOUR
T1 - Well-posedness of domain integral equations for a dielectric object in homogeneous background
AU - Beurden, van, M.C.
AU - Eijndhoven, van, S.J.L.
PY - 2008
Y1 - 2008
N2 - Abstract An analysis of the mapping properties of three commonly used domain integro–differential operators
for electromagnetic scattering by an inhomogeneous dielectric object embedded in a homogeneous background is
presented in the Laplace domain. The corresponding three integro–differential equations are shown to be equivalent
and well-posed under finite-energy conditions. The analysis allows for non-smooth changes, including edges and
corners, in the dielectric properties. The results are obtained via the Riesz–Fredholm theory, in combination with
the Helmholtz decomposition and the Sobolev embedding theorem.
AB - Abstract An analysis of the mapping properties of three commonly used domain integro–differential operators
for electromagnetic scattering by an inhomogeneous dielectric object embedded in a homogeneous background is
presented in the Laplace domain. The corresponding three integro–differential equations are shown to be equivalent
and well-posed under finite-energy conditions. The analysis allows for non-smooth changes, including edges and
corners, in the dielectric properties. The results are obtained via the Riesz–Fredholm theory, in combination with
the Helmholtz decomposition and the Sobolev embedding theorem.
U2 - 10.1007/s10665-008-9218-2
DO - 10.1007/s10665-008-9218-2
M3 - Article
VL - 62
SP - 289
EP - 302
JO - Journal of Engineering Mathematics
JF - Journal of Engineering Mathematics
SN - 0022-0833
IS - 3
ER -