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WEI Ying-jie, GAO Wen-jie
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Abstract: On the basis of constructing the functions of class Sα it is proved that the viscosity solutions of parabolic equations belong to the functions of class Sα under certain conditions. Thus the discu ssion of studying viscosity solutions is converted to that of studying the functions of class Sα. The Aleksandrov-Bakel'man-Pucci-Krylov-Tso maximum principle is generalized to a more general one and it is proved that the functions of class Sα obey the generalized Aleksandrov-Bakel'man-Pucci-Krylov-T so maximum principle, by means of which some regularity results to the viscosity solutions of fully nonlinear parabolic equations are obtained.
Key words: maximum principle, viscosity solutions, regularity
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WEI Ying-jie, GAO Wen-jie. Generalization of Aleksandrov-Bakel'man-Pucci-Krylov-Tsomaximum principle and its application to viscosity solutions[J].J4, 2004, 42(03): 317-322.
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http://xuebao.jlu.edu.cn/lxb/EN/Y2004/V42/I03/317
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