Some $L_{p}$-estimates for elliptic and parabolic operators with measurable coefficients

Details Some $L_{p}$-estimates for elliptic and parabolic operators with measurable coefficients Some $L_{p}$-estimates for elliptic and parabolic operators with measurable coefficients

2012-01-22

arxiv.org/abs/1201.4573v1

Mathematics

Analysis of PDEs

23 pages, submitted

Scientific paper

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.

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