摘要：

We consider S-2-valued maps on a domain Omega subset of R-N minimizing a perturbation of the Dirichlet energy with vertical penalization in Omega and horizontal penalization on partial derivative Omega. We first show the global minimality of universal constant configurations in a specific range of the physical parameters using a Poincare-type inequality. Then we prove that any energy minimizer takes its values into a fixed half-meridian of the sphere S-2 and deduce uniqueness of minimizers up to the action of the appropriate symmetry group. We also prove a comparison principle for minimizers with different penalizations. Finally, we apply these results to a problem on a ball and show radial symmetry and monotonicity of minimizers. In dimension N = 2 our results can be applied to the Oseen-Frank energy for nematic liquid crystals and the micromagnetic energy in a thin-film regime.

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