Armstrong–Silvestre–Smart's optimal exponent conjecture for viscosity supersolutions

Let $\lambda\leq\Lambda$ be positive constants, and let $\varepsilon$ be the exponent in the $W^{2,\varepsilon}$ estimate for viscosity supersolutions of

$$\mathcal{M}^{-}_{\lambda,\Lambda}(D^2u)\leq 0$$

in $B_1\subset\mathbb{R}^n$, namely the estimate asserting that

$$\left|\left\{x\in B_{1/2}:\underline\Theta(u,B_1)(x)>t\right\}\right|\leq Ct^{-\varepsilon}.$$

Armstrong–Silvestre–Smart's conjecture. The optimal exponent in this estimate is

$$\varepsilon=2(\Lambda/\lambda+1)^{-1}.$$

An explicit example shows that the exponent cannot be larger than this value, so the conjecture asserts sharpness of the known upper bound for the decay exponent. Its resolution is not specified in the supplied text.