Electron. J. Diff. Equ., Vol. 2015 (2015), No. 96, pp. 1-6.

Holder continuity with exponent $(1+\alpha )/2$ in the time variable for solutions of parabolic equations

Junichi Aramaki

Abstract:
We consider the regularity of solutions for some parabolic equations. We show Holder continuity with exponent $(1+\alpha )/2$, with respect to the time variable, when the gradient in the space variable of the solution has the Holder continuity with exponent $\alpha $.

Submitted February 16, 2015. Published April 13, 2015.
Math Subject Classifications: 35A09, 35K10, 35D35.
Key Words: Holder continuity; parabolic equation.

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Junichi Aramaki
Division of Science
Faculty of Science and Engineering
Tokyo Denki University,
Hatoyama-machi, Saitama 350-0394, Japan
email: aramaki@mail.dendai.ac.jp

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