JournalsjemsVol. 18, No. 6pp. 1321–1338

Estimates on elliptic equations that hold only where the gradient is large

  • Cyril Imbert

    Université Paris-Est Créteil Val de Marne, France

  • Luis Silvestre

    University of Chicago, USA
Estimates on elliptic equations that hold only where the gradient is large cover
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Abstract

We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the Hölder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.

Cite this article

Cyril Imbert, Luis Silvestre, Estimates on elliptic equations that hold only where the gradient is large. J. Eur. Math. Soc. 18 (2016), no. 6, pp. 1321–1338

DOI 10.4171/JEMS/614