Some monotonicity results for minimizers in the calculus of variations
  We obtain monotonicity properties for minima and stable solutions of general energy functionals of the type $$ \int F(\nabla u, u, x) dx $$ under the assumption that a certain integral grows at most quadratically at infinity. As a consequence we obtain several rigidity results of global solutions in low dimensions. 
Ovidiu Savin and Enrico Valdinoci
math.AP