Estimates in generalized Morrey spaces for linear parabolic systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:452

Article

McBride, Matt¹ 

[1] Mississippi State Univ, Dept Math & Stat, 175 Presidents Circle, Mississippi State, MS 39762 USA

关键词: Morrey spaces;    Regularity;    Parabolic systems;   

DOI  :  10.1016/j.jmaa.2017.03.021

来源: Elsevier

【 摘 要 】

In this study, we consider the parabolic system u(t)(i) - D-alpha (a(ij)(alpha beta)D(beta)u(j)) = - div f(i) in the generalized Morrey Space L-phi(2,lambda), where we aim to understand the regularity of the solutions to this system. We show that: (1) if a(ij)(alpha beta) is an element of C((Q(T)) over bar), then Du is an element of L-phi(2,lambda); and (2) if a(ij)(alpha beta) is an element of VMO(Q(T)), then Du is an element of L-phi(2,lambda). Moreover, we obtain estimates of the gradient for the solutions to the system, thereby showing the regularity of the solutions. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free