Estimates on elliptic equations that hold only where the gradient is large
Cyril Imbert
Université Paris-Est Créteil Val de Marne, FranceLuis Silvestre
University of Chicago, USA
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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