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

2012/01/22 by Н. В. Крылов, Krylov, N. V.
Mathematics · #35J15 #35K10 #60H10 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1201.4573

openalex publication_date 2012/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeDKL. The first type is an estimate of the γth norm of the second-order derivatives, where γ∈(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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