Homogenization of a class of singular elliptic problems in two-component domains

This paper deals with the homogenization of a quasilinear elliptic problem having singular lower order term and posed in two-component domain an ε-periodic imperfect interface. We prescribe Dirichlet condition on exterior boundary, while we assume that continuous heat flux is proportional to jump solution interface via function ε γ . prove result for − 1 < by means periodic unfolding method (see SIAM J. Math. Anal. 40 (2008) 1585–1620 The Periodic Unfolding Method (2018) Springer), adapted domains (J. Sci. 176 (2011) 891–927). One main tools process convergence suitable auxiliary linear problem, associated weak limit sequence { u } solutions, as → 0. More precisely, our shows gradient behaves like which allows us pass term, study near its singularity, accurate priori estimate.