- 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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