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arXiv · 1209.1517

Some monotonicity results for minimizers in the calculus of variations

Ovidiu Savin·Enrico Valdinoci
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Abstract

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.

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Ovidiu Savin, Enrico Valdinoci. 2012-09-07. Some monotonicity results for minimizers in the calculus of variations. https://arxiv.org/abs/1209.1517

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