10-139 Marcelo Montenegro and Enrico Valdinoci
Pointwise estimates and monotonicity formulas without maximum principle (247K, pdf) Sep 5, 10
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Abstract. We study a second order elliptic partial differential equation for which a maximum principle is not available and whose nonlinearity is not $C^1$. We discuss the role of a pointwise gradient bound, of which we study the optimal constant. As a consequence, we derive a monotonicity estimate near flat points of the free boundary of a minimizer.

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