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.
Some monotonicity results for minimizers in the calculus of variations / O. Savin, E. Valdinoci. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 264:10(2013), pp. 2469-2496.
Some monotonicity results for minimizers in the calculus of variations
E. ValdinociUltimo
2013
Abstract
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.
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