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

Abstract

AbstractIn 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 fromRN+1{{\mathbb{R}}}^{N+1}, with corrugated bounder, which degenerates to an open bounded set inRN{{\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 inNN-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.