Acta Scientiarum Naturalium Universitatis Pekinensis

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Local Regularity for the Linear Second-Order Parabolic Equation in Nondivergence Form

YAO Fengping1, ZHANG Kejing2   

  1. 1. Department of Mathematics, School of Sciences, Shanghai University, Shanghai 200436; 2.School of Mathematical Sciences, Peking University, Beijing 100871;
  • Received:2010-03-03 Online:2011-03-20 Published:2011-03-20



  1. 1. 上海大学理学院数学系,上海 200436; 2. 北京大学数学科学学院, 北京 100871;

Abstract: By developing the method of Acerbi et al, the authors obtain local regularity in Orlicz spaces for the linear second-order parabolic equations with small BMO coefficients in nondivergence form. Such regularity estimates can be applied to the study of the existence of solutions in W2,1p.

Key words: second-order, nondivergence, parabolic, regularity, small BMO, Orlicz spaces

摘要: 发展了Acerbi 等的方法, 得到了一类具有小 BMO 系数的二阶线性非散度型抛物方程解的二阶偏导数在Orlicz 空间中的局部正则性估计。这种正则性估计可以应用于 W2,1p解的存在性问题。

关键词: 二阶, 非散度型, 抛物方程, 正则性估计, 小BMO, Orlicz空间

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