We consider a nonlinear Robin problem for the Poisson equation in an unbounded periodically perforated domain. The domain has a periodic structure, and the size of each cell is determined by a positive parameter δ. The relative size of each periodic perforation is determined by a positive parameter ε. Under suitable assumptions, such a problem admits a family of solutions which depends on ε and δ. We analyse the behaviour the energy integral of such a family as (ε, δ) tends to (0, 0) by an approach that represents an alternative to asymptotic expansions and classical homogenization theory.

中文翻译：

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具有非线性周期性 Robin 边界条件的双参数均匀化问题的能量积分的渐近行为

我们在无界周期性穿孔域中考虑泊松方程的非线性 Robin 问题。域具有周期性结构，每个单元的大小由一个正参数决定δ. 每个周期性穿孔的相对尺寸由一个正参数确定ε. 在适当的假设下，这样的问题有一系列解决方案，这些解决方案取决于ε和δ. 我们分析这样一个家庭的能量积分的行为，如（ε,δ) 趋向于 (0, 0)，这种方法代表了渐近展开和经典同质化理论的替代方案。