Junichi Aramaki
Abstract:
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 email: aramaki@mail.dendai.ac.jp |
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