Gamma-convergence of a shearlet-based Ginzburg-Landau energy

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 L2-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 and we demonstrate that its anisotropy can be controlled by weighting the underlying shearlet transforms according to their directional parameter.