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# Mathematical Research Letters

## Volume 27 (2020)

### Number 1

### Polynomial decay in $W^{2,\varepsilon}$ estimates for viscosity supersolutions of fully nonlinear elliptic equations

Pages: 189 – 207

#### Author

#### Abstract

We prove $W^{2,\varepsilon}$ estimates for viscosity supersolutions of fully nonlinear, uniformly elliptic equations where ε decays polynomially with respect to the ellipticity ratio of the equations. Our result is related to a conjecture of Armstrong–Silvestre–Smart [*Comm. Pure Appl. Math.* **65** (2012), no. 8, 1169–1184] which predicts a linear decay for $\varepsilon$ with respect to the ellipticity ratio of the equations.

The research of the author was supported in part by the National Science Foundation under grant DMS-1764248.

Received 25 June 2018

Accepted 9 September 2018