On linear elliptic and parabolic equations with growing drift in Sobolev spaces without weights

2009/02/17 by Н. В. Крылов, Krylov, N. V.
Computer Science · Mathematics · #35J15 #35K10 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0902.3006

openalex publication_date 2009/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider uniformly elliptic and parabolic second-order equations with bounded zeroth-order and bounded VMO leading coefficients and possibly growing first-order coefficients. We look for solutions which are summable to the p-th power with respect to the usual Lebesgue measure along with their first and second-order derivatives with respect to the spatial variable.

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