TY - JOUR

T1 - On homogenization of the stationary Periodic Maxwell system in a bounded domain

AU - Suslina, T. A.

N1 - Suslina, T.A. On the Homogenization of the Stationary Periodic Maxwell System in a Bounded Domain. Funct Anal Its Appl 53, 69–73 (2019). https://doi.org/10.1007/s10688-019-0251-x

PY - 2019/6/1

Y1 - 2019/6/1

N2 - In a bounded domain O ⊂ ℝ3 of class C1,1, the stationary Maxwell system with boundary conditions of perfect conductivity is considered. It is assumed that the dielectric permittivity and the magnetic permeability are given by η(x/ε) and μ(x/ε), where η and μ are symmetric bounded positive definite matrix-valued functions periodic with respect to some lattice in ℝ3. Here ε > 0 is a small parameter. It is known that, as ε > 0, the solutions of the Maxwell system weakly converge in L2(O) to the solutions of the homogenized Maxwell system with constant effective coefficients. Classical results are improved and approximations for the solutions in the L2(O)-norm with error estimates of operator type are found.

AB - In a bounded domain O ⊂ ℝ3 of class C1,1, the stationary Maxwell system with boundary conditions of perfect conductivity is considered. It is assumed that the dielectric permittivity and the magnetic permeability are given by η(x/ε) and μ(x/ε), where η and μ are symmetric bounded positive definite matrix-valued functions periodic with respect to some lattice in ℝ3. Here ε > 0 is a small parameter. It is known that, as ε > 0, the solutions of the Maxwell system weakly converge in L2(O) to the solutions of the homogenized Maxwell system with constant effective coefficients. Classical results are improved and approximations for the solutions in the L2(O)-norm with error estimates of operator type are found.

KW - periodic differential operators

KW - homogenization

KW - operator error estimates

KW - stationary Maxwell system

UR - https://link.springer.com/article/10.1007/s10688-019-0251-x

M3 - Article

VL - 53

SP - 69

EP - 73

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 1

ER -