Estimates in the Generalized Morrey Spaces for Linear Parabolic Systems

2008/11/20 by Matthew Scott McBride, McBride, Matthew
Mathematics · #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.0811.3360

openalex publication_date 2008/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper is to study the parabolic system u_tⁱ-D_α(a_ij^αβD_βu^j)=-div fⁱ in the generalized Morrey Space L_ϕ^2,λ . We would like to understand the regularity of the solutions of this system. It will be shown that 1: if a_ij^αβ∈ C(Q_T) then Du∈ L_ϕ^2,λ, and 2: if a_ij^αβ∈ VMO(Q_T) then Du∈ L_ϕ^2,λ. Moreover we will be able to obtain estimates on the gradient of the solutions to the system, which will tell us about the regularity of the solutions.

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