Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (3): 527-538.doi: 10.1016/S0252-9602(09)60051-5

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THE HÖLDER CONTINUITY OF A CLASS OF 3-DIMENSION ULTRAPARABOLIC EQUATIONS

 WANG Wen-Dong, ZHANG Li-Qun   

  1. Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2008-08-25 Online:2009-05-20 Published:2009-05-20
  • Supported by:

    The research is partially supported by the NSF of China (10325104)

Abstract:

We obtained the Cα continuity for weak solutions of a class of ultraparabolic equations with measurable coefficients of the form

∂ t , u= ∂ x (a(x, y, t) ∂ x , u )+b0(x, y, t) ∂ x u+b(x, y, t) ∂ y u,

which generalized our recent results on KFP equations.

Key words: hypoelliptic, ultraparabolic equations, Hölder regularity

CLC Number: 

  • 35K65
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