### Abstract

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.

Original language | English |
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Pages (from-to) | 915-944 |

Number of pages | 30 |

Journal | Differential and Integral Equations |

Volume | 5 |

Issue number | 4 |

Publication status | Published - 1992 Jul |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics