Abstract
In this paper, the application of the G class of functions in the parabolic class is considered. The regularity of the solution for the first boundary value problem of parabolic equation in divergence form is proved.
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Li, S. H., Liu, X. G., The G class functions and its application, Acta Math. Sinica (N. S.), 2000, 15 (1):1–14.
Chen, Y. Z., C 1,a regularity of viscosity solution for fully nonlinear elliptic partial differential equation under natural structure conditions, J. Partial Differential Equations, 1993, 6(3):193–216
Chen, Y. Z., Wu, L. C., Elliptic Partial Differential Equations and Systems of Second Order, Science Press, Beijing China, 1991.
Dong, G. C., Nonlinear partial differential equation of second order, Transl. Math. Monogr., Vol. 95, 1993.
Korolev, A. G., On boundedness of generalized solutions of elliptic differential equation with nonlinear power nonlinearities, Math. USSR-Sb, 1990, 66:83–106.
Lieberman, G. M., The natural generaliztion of the natural conditions of Ladyzhenskaya and Ural’tseva for elliptic equations, Comm. Partial Differential Equations, 1991, 16 (2&3):311–361.
Lieberman, G. M., Bounday and initial regularity for solution of degeneate parabolic equations, Nonlinear Analysis, 1993, 20:557–569.
Skrypnik, I. V., On the Hölder property for functions from the class B q,s, Ukrainian Math. J., 1995, 45:1020–1028.
Wang, G. L., Harnack Inequalities for Function in De Giorgi Parabolic Class, Partial Differential Equation, Springer-Verlag, New York, 1986, 182–201.
Ladyzhenskaya, O. A., Solonnikov, V. A., Ural’tseva, N. N., Linear and Quasilinear Equation of Parabolic Type, Nauka, Moscow, 1967.
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Project supported by ZJPNC (198013), NNSFC (79790130) and Zhejiang Univ., Cao Guangbiao Foundation.
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Shenghong, L. Application of the G class of functions in the parabolic class. Appl. Math. Chin. Univ. 15, 297–301 (2000). https://doi.org/10.1007/s11766-000-0054-z
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DOI: https://doi.org/10.1007/s11766-000-0054-z