## Abstract

We are concerned with optimal regularity theory in weighted Sobolev spaces for discontinuous non-linear parabolic problems in divergence form over a non-smooth, bounded domain. Assuming smallness in BMO of the principal part of the non-linear operator and flatness in Reifenberg sense of the boundary, we establish a global weighted W1,p estimate for the weak solutions of such problems by proving that the spatial gradient and the non-homogeneous term belong to the same weighted Lebesgue space. The result is new in the settings of non-linear parabolic problems.

Original language | English |
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Pages (from-to) | 765-778 |

Number of pages | 14 |

Journal | Bulletin of the London Mathematical Society |

Volume | 45 |

Issue number | 4 |

DOIs | |

State | Published - Aug 2013 |

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