We introduce two shearlet-based Ginzburg–Landau energies, based on the continuous and the discrete shearlet transform. The energies result from replacing the elastic energy term of a classical Ginzburg–Landau energy by the weighted $L^2$-norm of a shearlet transform. The asymptotic behaviour of sequences of these energies is analysed within the framework of Γ-convergence and the limit energy is identified. We show that the limit energy of a characteristic function is an anisotropic surface integral over the interfaces of that function. We demonstrate that the anisotropy of the limit energy can be controlled by weighting the underlying shearlet transforms according to their directional parameter.

我们基于连续的和离散的小波变换引入了两种基于小波的Ginzburg-Landau能量。能量是通过将加权后的经典Ginzburg-Landau能量的弹性能项替换为${\mathrm{大号}}^2$-剪切波变换的范数。在Γ收敛的框架内分析了这些能量序列的渐近行为，并确定了极限能量。我们表明，特征函数的极限能量是该函数界面上的各向异性表面积分。我们证明，可以通过根据其方向参数加权基础的Slicelet变换来控制极限能量的各向异性。