Pointwise Estimates and Monotonicity Formulas without Maximum Principle

Marcelo Montenegro; Enrico Valdinoci

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 boundary.

Author information

Contact details are reproduced from the original publication and may be historical.

Marcelo Montenegro

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

msm@ime.unicamp.br

Enrico Valdinoci

Dip. di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy

enrico@math.utexas.edu

Keywords

Elliptic PDEs
a-priori estimates
monotonicity formula
free boundary

Mathematics Subject Classification

35B09, 35B45, 35J25, 35J61, 35R35

Suggested citation

M. Montenegro, E. Valdinoci. “Pointwise Estimates and Monotonicity Formulas without Maximum Principle.” Journal of Convex Analysis 20 (2013), No. 1, 199–220.