2012/09/07 by Ovidiu Savin, Enrico Valdinoci, Savin, Ovidiu +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.1209.1517
arxiv created 2012/09/07 · arxiv updated 2012/09/10
We obtain monotonicity properties for minima and stable solutions of general energy functionals of the type ∫ F(∇ 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.