Parabolic
An entropy approach to parabolic ABP
Astra’s proof of the kinetic Krylov–Safonov theorem is based on a novel approach to the ABP estimate. It derives an entropy estimate for the adjoint equation by regularising along an auxiliary flow and exploiting entropy dissipation.
A parabolic analogue of the Pucci conjecture
In the parabolic setting the sharp range for the exponent is
\[
p>\max\left\{\frac{n+2}{2},\,n[1-(n-1)\delta]\right\}.
\]