Some monotonicity results for minimizers in the calculus of variations
classification
🧮 math.AP
keywords
monotonicityobtainresultssolutionsassumptioncalculuscertainconsequence
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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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