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Journal of Convex Analysis 20 (2013), No. 1, 199--220
Copyright Heldermann Verlag 2013

Pointwise Estimates and Monotonicity Formulas without Maximum Principle

Marcelo Montenegro
Dep. de Matemática, Universidade Estadual de Campinas -- IMECC, Rua Sérgio Buarque de Holanda 651, Campinas-SP CEP 13083-859, Brazil

Enrico Valdinoci
Dip. di Matematica, Universitŕ di Milano, Via Saldini 50, 20133 Milano, Italy

We study a second order elliptic partial differential equation for which a maximum principle is not available and whose nonlinearity is not C1. We discuss the role of a pointwise gradient bound and we derive a monotonicity estimate near flat points of the free boundary.

Keywords: Elliptic PDEs, a-priori estimates, monotonicity formula, free boundary.

MSC: 35B09, 35B45, 35J25, 35J61, 35R35

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