A Nash Type Result for Divergence Parabolic Equation Related to H?rmander＇s Vector Fields

• 来源期刊: 偏微分方程（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 341-376
• 页数: 36页
• 分类号: O175.27
• 语种: 英文
• DOI: 10.4208/jpde.v33.n4.3

摘要

In this paper we consider the divergence parabolic equation with bound-ed and measurable coefficients related to Hormander＇s vector fields and establish a Nash type result,i.e.,the local Holder regularity for weak solutions.After deriving the parabolic Sobolev inequality,(1,1) type Poincare inequality of Hormander＇s vec-tor fields and a De Giorgi type Lemma,the Holder regularity of weak solutions to the equation is proved based on the estimates of oscillations of solutions and the isomor-phism between parabolic Campanato space and parabolic Holder space.As a conse-quence,we give the Harnack inequality of weak solutions by showing an extension property of positivity for functions in the De Giorgi class.