Abstract
Let A and B satisfy the structural conditions (2), the local Hölder continuity interior toQ=G×(0,T) is proved for the generalized solutions of quasilinear parabolic equations as follows:u t -divA(x, t, u, ∇u)+B(x, t, u, ∇u)=0
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural' ceva, Linear and quasilinear equations of parabolic type,Trans. Amer. Math. Munogr.,23, 6 (1968), 731–747.
Wang Xiangdong, Liang Xiting and Lang Xuesin, The boundedness for generalized solutions of quasilinear parabolic equations,Mathematica Applicata,5, 2 (1992), 88–96. (in Chinese).
J. Moser, A Harnack inequality for parabolic differential equations,Comm. Pure Appl. Math.,17, 9 (1964), 131–134.
Author information
Authors and Affiliations
Additional information
Communicated by Zhang Shisheng
Rights and permissions
About this article
Cite this article
Xiangdong, W., Xiting, L. The hölder continuity of generalized solutions of a class quasilinear parabolic equations. Appl Math Mech 19, 573–583 (1998). https://doi.org/10.1007/BF02453413
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02453413