Optimal parabolic Aleksandrov exponent

Determine the exact critical Lebesgue exponent for the parabolic Aleksandrov maximum principle with measurable non-divergence-form coefficients in the general case.

Background

The paper compares kinetic Aleksandrov estimates with their elliptic and parabolic counterparts. Scaling and radial examples provide lower bounds for the critical exponent, while reverse Hölder estimates establish admissible exponents below the classical scaling dimension in some regimes. The authors state that these results do not determine the exact exponent for general parabolic coefficients.