Reverse Holder inequalities for singular parabolic equations near the boundary

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Parviainen, Mikko

关键词: Boundary value problem;    Gehring lemma;    Global higher integrability;    Initial value problem;    Singular systems;   

DOI  :  10.1016/j.jde.2008.06.013

来源: Elsevier

【 摘 要 】

We show that weak solutions to a singular parabolic partial differential equation globally belong to a higher Sobolev space than assumed a priori. To this end, we prove that the gradients satisfy a reverse Holder inequality near the boundary. The results extend to singular parabolic systems as well. Motivation for studying reverse Holder inequalities comes partly from applications to regularity theory. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free