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 solutions to degenerate parabolic variational inequalities are locally Hölder continuous. Using a difference quotient method and Moser type iteration it is then proved that the gradient of a solution is locally bounded. Finally using iteration and scaling it is shown that the gradient of the solution satisfies a Campanato type integral inequality and is locally Hölder continuous.
|Number of pages||30|
|Journal||Differential and Integral Equations|
|Publication status||Published - 1992 Jul|
All Science Journal Classification (ASJC) codes
- Applied Mathematics