We shall show that the Poincare type inequality holds for the weak solution of a parabolic equation. The key is to control the norm of the first derivative of the weak solution with respect to the time variable. The inequality is necessary to get an estimate in the Campanato space for general parabolic equations.
Submitted December 24, 2015. Published July 28, 2016.
Math Subject Classifications: 35A09, 35K10, 35D35.
Key Words: Poincare type inequality; weak solution; 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
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