as $\eps^{2/3}L^{1/3}H$ [@B9_KohnMuller92; @B9_KohnMuller94], the same result as in Theorem \[Theorem:K1\]. It was later shown that the minimizers of their functional are asymptotically self similar [@B9_Conti00]. Kohn and Müller also studied a softer problem, in which the Dirichlet boundary condition is eliminated and instead the term $\beta \|u(0,\cdot)\|_{H^{1/2}((0,H))}^2$ is added to the energy $E_\mathrm{KM}$, where $u(0,\cdot)$ is the trace of the deformation on the $x_1=0$ boundary. Physically, this corresponds to the elastic energy of the material “outside the domain”. Their results, which were completed in [@B9_Conti2006; @B9_Zwicknagl], state that, for small $\eps$ and $\beta$, the optimal energy scales as $$\label{eqscalingKMbeta}
  \min\{\eps^{2/3}L^{1/3}H, \eps^{1/2}\beta^{1/2}L^{1/2}H\}\,.$$ The first option corresponds to a branched pattern, the second one to a laminar, one-dimensional pattern, in which the interfaces are exactly parallel to $e_1$ and the incompatibility is accommodated by the boundary term. We remark that the minimum in the assertion of Theorem 1 in [@B9_Conti2006] misses a term proportional to $\eps^{1/2}$. This term, which was correctly identified in [@B9_Zwicknagl], arises since, at the end of the proof, one can only choose $l'=\min\{1/\beta, \eps^{-1/2}\}$ and is only relevant for large values of $\eps$. The correct bound is $J_{\eps,\beta}\ge c \min\{\eps^{1/2}\beta^{1/2}L^{1/2}H,
\eps^{2/3}L^{1/3}H, \eps^{1/2}H^{3/2}, \beta H^2\}$.

Variants, in which 