Some Lp-estimates for elliptic and parabolic operators with measurable coefficients

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Abstract

We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of Lp-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 γth norm of the second-order derivatives, where 2 (0; 1), and the second type deals with estimates of the resolvent operators in Lp when the first-order coefficients are summable to an appropriate power.

Original languageEnglish (US)
Pages (from-to)2073-2090
Number of pages18
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume17
Issue number6
DOIs
StatePublished - Dec 13 2012

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