which is equivalent to $$\label{eqepsalphaL}
  \eps \le \alpha L\,.$$

We now start the construction. We will focus on $\Omega'=(0,L/2)\times (0,H)$, the other part is analogous (with minor sign changes in the formulas). The basic idea in the construction is to have coarse folds in the central part, which then refine in a self-similar way approaching to the boundary, up to a point where a different construction for the boundary layer is needed, see Figure \[fig:1\].

Let $N\in\N\setminus\{0\}$ be the number of oscillations in the center, $\theta\in(1/4,1/2)$ a geometric factor, both will be chosen below. We cut the domain in vertical stripes, so that in each of them, say $(x_{i+1},x_i)\times(0,H)$, the construction will be $h_i$-periodic in the $y$ direction. We define $$x_i = \frac{L}{2}\theta^{i}\quad \text{ and } \quad  h_i= \frac{H}{2^{i}N}$$ and denote the width of the $i$-th stripe by $\ell_i=\theta^{i}(1-\theta)\frac{L}{2}$.

Since the construction in Lemma \[eqconstronerecttheo2\] requires $h_i \leq \ell_i$, we need to stop this procedure at a finite $\tau$, defined as the largest integer $i$ with $h_i\leq \ell_i$. Further, we need to choose $N$ such that $H/N\le (1-\theta)L/2$, to be able to start.

For $i\in [0,\tau]\cap \N$ and $y\in (0,H)$, we set $$\label{eqvperiodiclines}
  v(x_i,y)={\ensuremath{\begin{pmatrix}x_i \\ y+\alpha \vartheta_{h_i}(y) \end{pmatrix}}}\,.$$ This permits 