Affiliations: [a] Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India | [b] TIFR Center for Applicable Mathematics, Bangalore, 560065, India
Abstract: In the present article, we study the homogenization of a second-order elliptic PDE with oscillating coefficients in two different domains, namely a standard rectangular domain with very general oscillations and a circular type oscillating domain. Further, we consider the source term in L1 and hence the solutions are interpreted as renormalized solutions. In the first domain, oscillations are in horizontal directions, while that of the second one is in the angular direction. To take into account the type of oscillations, we have used two different types of unfolding operators and have studied the asymptotic behavior of the renormalized solution of a second-order linear elliptic PDE with a source term in L1. In fact, we begin our study in oscillatory circular domain with oscillating coefficients and L2 data which is also new in the literature. We also prove relevant strong convergence (corrector) results. We present the complete details in the context of circular domains, and sketch the proof in other domain.
