On one-space dimensional parabolic equations with measurable coefficients: Sobolev estimates and the Alexandrov maximum principle

Hongjie Dong, Zongyuan Li

Let $0<\kappa <1$ and set $p_{+}=2/(1-\kappa )$ and $p_{-}=2/(1+\kappa )$. We construct a coefficient $\kappa \le a\le {\kappa }^{-1}$, smooth outside a compact set of Lebesgue measure zero, for which the $W^{1,2}_{…