Parabolic equations with partially VMO coefficients and boundary value problems in Sobolev spaces with mixed norms

2007/06/03 by Doyoon Kim, Kim, Doyoon
Computer Science · Mathematics · #35A05 #35K10 #35K20 #35R05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.0706.0329

openalex publication_date 2007/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Second order parabolic equations in Sobolev spaces with mixed norms are studied. The leading coefficients (except a¹¹) are measurable in both time and one spatial variable, and VMO in the other spatial variables. The coefficient a¹¹ is measurable in time and VMO in the spatial variables. The unique solvability of equations in the whole space is applied to solving Dirichlet and oblique derivative problems for parabolic equations defined in a half-space.

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