English

Some monotonicity results for minimizers in the calculus of variations

Analysis of PDEs 2012-09-10 v1

Abstract

We obtain monotonicity properties for minima and stable solutions of general energy functionals of the type F(u,u,x)dx \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.

Keywords

Cite

@article{arxiv.1209.1517,
  title  = {Some monotonicity results for minimizers in the calculus of variations},
  author = {Ovidiu Savin and Enrico Valdinoci},
  journal= {arXiv preprint arXiv:1209.1517},
  year   = {2012}
}