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 RN+1{{\mathbb{R}}}^{N+1}, with corrugated bounder, which degenerates to an open bounded set in RN{{\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 NN-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.

Keywords

• quasilinear elliptic equations
• thin domains
• homogenization
• unfolding operator method
• 35b25
• 35b27
• 35b40
• 35j92