Article Contents
Article Contents

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

• 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 [1]. 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.
Mathematics Subject Classification: 35J15, 35K10, 60H10.

 Citation:

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