| THE BERNSTEIN ESTIMATES OF VISCOSITY SOLUTIONS OF LINEAR PARABOLIC EQUATIONS |
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| 作者姓名： | 詹毅 |
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| 作者单位： | Department of Applied Mathematics，Tsinghua University，Beijing 100084，China |
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| 摘 要： | ＴＨＥＢＥＲＮＳＴＥＩＮＥＳＴＩＭＡＴＥＳＯＦＶＩＳＣＯＳＩＴＹＳＯＬＵＴＩＯＮＳＯＦＬＩＮＥＡＲＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＳＺＨＡＮＹＩ（詹毅）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉ...
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| 收稿时间： | 11 April 1992 |
The Bernstein estimates of viscosity solutions of linear parabolic equations |
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| Yi Zhan.THE BERNSTEIN ESTIMATES OF VISCOSITY SOLUTIONS OF LINEAR PARABOLIC EQUATIONS[J].Acta Mathematicae Applicatae Sinica,1995,11(3):255-262. |
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| Authors: | Yi Zhan |
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| Institution: | (1) Department of Applied Mathematics, Tsinghua University, 100084 Beijing, China |
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| Abstract: | This paper is concerned with the Bernstein estimates of viscosity solutions of the Cauchy problems for linear parabolic equations. The techniques of viscosity solution method given by H.Ishii and P.L. Lions in 1] allow us to deduce the estimates without differentiating the equation,which is in a way completely different from the classical one. We mainly get the estimate of under the corresponding assumptions on the smoothness of solutions and the known functions in the equation. |
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| Keywords: | Bernstein estimates viscosity solution linear parabolic equations |
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