SOME L-p-ESTIMATES FOR ELLIPTIC AND PARABOLIC OPERATORS WITH MEASURABLE COEFFICIENTS

作者：Krylov N V^*

来源：Discrete and Continuous Dynamical Systems-Series B, 2012, 17(6): 2073-2090.

DOI：10.3934/dcdsb.2012.17.2073

• Elliptic and parabolic equations
• measurable coefficients
• occupation measures for diffusion processes

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 equations in [1]. The first type is an estimate of the gamma th norm of the second-order derivatives, where gamma epsilon (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.

• 出版日期2012-9