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arXiv · 1306.2429

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

Cyril Imbert·Luis Silvestre
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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 H{ö}lder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.

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Cyril Imbert, Luis Silvestre. 2016-05-09. Estimates on elliptic equations that hold only where the gradient is large. https://doi.org/10.4171/jems%2F614

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