By means of an inequality of Poincaré type, a weak Harnack inequality for the gradient of a solution and an integral inequality of Campanato type, it is shown that a solution to certain degenerate parabolic system is locally Hölder continuous. The system is a generalization of p-Laplacian system. Using a difference quotient method and Moser type iteration it is then proved that the gradient of a solution is locally bounded. Finally using the iteration and scaling it is shown that the gradient of the solution satisfies a Campanato type integral inequality and is locally Hölder continuous.
Bibliographical noteFunding Information:
The authors thank the referees. The first author was supported by Korea Research Foundation Grant (KRF-2001-015-DP0020).
All Science Journal Classification (ASJC) codes
- Applied Mathematics