Curl-Free Ginzburg-Landau Vortices
  For certain nonlinear elliptic PDE problems in two dimensions, the classical isoperimetric inequality produces a sharp inequality that violates a Pohozaev identity except for radial symmetric, decreasing solutions. A generalized version of this technique is used here to prove radial symmetry of curl-free Ginzburg-Landau vortices. 
Sagun Chanillo and Michael Kiessling (Dept. Math., Rutgers Univ)