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 boimdary.
Pointwise estimates and monotonicity formulas without maximum principle / M. Montenegro, E. Valdinoci. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - 20:1(2013), pp. 199-220.
Pointwise estimates and monotonicity formulas without maximum principle
E. Valdinoci
2013
Abstract
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 boimdary.
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