Abstract

We study a second order elliptic partial differential equation for which a maximum principle is not available and whose nonlinearity is not C1C^1. 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
and: Istituto di Matematica Applicata e Tecnologie Informatiche, Consiglio Nazionale delle Ricerche, Via Ferrata, 1, 27100 Pavia, Italy

enrico@math.utexas.edu

Keywords

  • Elliptic PDEs
  • a-priori estimates
  • monotonicity formula
  • free boundary

Mathematics Subject Classification

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

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Suggested citation

M. Montenegro, E. Valdinoci. “Pointwise Estimates and Monotonicity Formulas without Maximum Principle.” Journal of Convex Analysis 20 (2013), No. 1, 199–220. https://doi.org/10.68381/jca20012

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press LLC.