Quasilinear problems with nonlinear boundary conditions in higher-dimensional thin domains with corrugated boundaries

Abstract In this work, we analyze the asymptotic behavior of a class of quasilinear elliptic equations defined in oscillating ( N + 1 ) \left(N+1) -dimensional thin domains (i.e., a family of bounded open sets from R N + 1 {{\mathbb{R}}}^{N+1} , with corrugated bounder, which degenerates to an open bounded set in R N {{\mathbb{R}}}^{N} ). We also allow monotone nonlinear boundary conditions on the rough border whose magnitude depends on the squeezing of the domain. According to the intensity of the roughness and a reaction coefficient term on the nonlinear boundary condition, we obtain different regimes establishing effective homogenized limits in N N -dimensional open bounded sets. In order to do that, we combine monotone operator analysis techniques and the unfolding method used to deal with asymptotic analysis and homogenization problems.