Corrector estimates for a class of imperfect transmission problems

Abstract

Based on previous homogenization results for imperfect transmission problems in two-component domains with periodic microstructure, we derive quantitative estimates for the difference between the microscopic and macroscopic solution. This difference is of order , where > 0 describes the periodicity of the microstructure and 2 (0; 1/2 ] depends on the transmission condition at the interface between the two components. The corrector estimates are proved without assuming additional regularity for the local correctors using the periodic unfolding method.