Symmetry and uniqueness of nonnegative solutions of some problems in the   halfspace
  We derive some 1-D symmetry and uniqueness or non-existence results for nonnegative solutions of some elliptic system in the halfspace $\R^N_+$ in low dimension. Our method is based upon a combination of Fourier series and Liouville theorems. 
A. Farina, N. Soave
math.AP