极值原理的推广及其在研究粘性解中的应用

Abstract

Abstract: On the basis of constructing the functions of class S_α it is proved that the viscosity solutions of parabolic equations belong to the functions of class S_α under certain conditions. Thus the discu ssion of studying viscosity solutions is converted to that of studying the functions of class S_α. 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 S_α 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

CLC Number:

O175

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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Generalization of Aleksandrov-Bakel'man-Pucci-Krylov-Tsomaximum principle and its application to viscosity solutions

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