Some $L_p$-estimates for elliptic and parabolic operators with measurable coefficients

Abstract

We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_p$-estimates for their solutions, which were recently used in the theory of fully nonlinear elliptic and parabolic second order equations in \cite{DKL}. The first type is an estimate of the $\gamma$th norm of the second-order derivatives, where $\gamma \in (0,1)$, and the second type deals with estimates of the resolvent operators in $L_p$ when the first-order coefficients are summable to an appropriate power.

arXiv comment23 pages, submitted