Acta mathematica scientia, Series B >
THE HÖLDER CONTINUITY OF A CLASS OF 3-DIMENSION ULTRAPARABOLIC EQUATIONS
Received date: 2008-08-25
Online published: 2009-05-20
Supported by
The research is partially supported by the NSF of China (10325104)
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
WANG Wen-Dong , ZHANG Li-Qun . THE HÖLDER CONTINUITY OF A CLASS OF 3-DIMENSION ULTRAPARABOLIC EQUATIONS[J]. Acta mathematica scientia, Series B, 2009 , 29(3) : 527 -538 . DOI: 10.1016/S0252-9602(09)60051-5
[1] Cinti C, Pascucci A, Polidoro S. Pointwise estimates for solutions to a class of non-homogenous Kolmogorov equations. Mathematische Annalen, 2008, 340(2): 237--264
[2] Cinti C, Polidoro S. Pointwise local estimates and Gaussian upper bounds for a class of uniformly subelliptic ultraparabolic operators. J Math Anal Appl, 2008, 338: 946--969
[3] Folland G B. Subellitic estimates and function space on nilpotent Lie groups. Ark Math, 1975, 13(2): 161--207
[4] Gilberg D, Trudinger N S. Elliptic Partial Differential Equations of Second Order. 3nd ed, Berlin: Springer-Verlag, 2001
[5] Lanconelli E, Polidoro S. On a class of hypoelliptic evolution operaters. Rend Sem Mat Univ Politec Torino, 1994, 52(1): 29--63
[6] Pascucci A, Polidoro S. The moser's iterative method for a class of ultraparabolic equations. Commun Contemp Math, 2004, 6(3): 395--417
[7] Wang W, Zhang L. The Cα regularity of a class of non-homogeneous ultraparabolic equations. http://arxiv. org/arXiv:math.AP/0711. 3411
[8] Wang W, Zhang L. The Cα regularity of a class of hypoelliptic ultraparabolic equations. http://arxiv.org/ arXiv: math. AP/0804. 4358v2
[9] Weber M. The fundamental solution of a degenerate partial differential equation of parabolic type. Trans Amer Math Soc, 1951, 71: 24--37
[10] Zhang L. The Cα reglarity of a class of ultraparabolic equations. http://arxiv.org/arXiv:math.AP/ 0510405v2
[11] Zhang L. The Cα reglarity of a class of ultraparabolic equations. Studies in Adv Math, Vol 42. AMS/IP, 2008: 619--622
[12] Xin Z P, Zhang L, Zhao J N. Global well-posedness for the two dimensional Prandtl's boundary layer equation.
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