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

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

YAO Fengping¹, ZHANG Kejing²

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

二阶线性非散度型抛物方程解的局部正则性估计

姚锋平¹,张克竞²

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

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 W^2,1_p.

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 W^2,1_p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

CLC Number:

O175

YAO Fengping,ZHANG Kejing. Local Regularity for the Linear Second-Order Parabolic Equation in Nondivergence Form[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

姚锋平,张克竞. 二阶线性非散度型抛物方程解的局部正则性估计[J]. 北京大学学报（自然科学版）.

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https://xbna.pku.edu.cn/EN/Y2011/V47/I2/208

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

二阶线性非散度型抛物方程解的局部正则性估计

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