## Abstract

This paper contains two results on the L^{p} regularity problem on Lipschitz domains. For second order elliptic systems and 1 < p < ∞, we prove that the solvability of the L^{p} regularity problem is equivalent to that of the L^{p}′ Dirichlet problem. For higher order elliptic equations and systems, we show that if p > 2, the solvability of the L^{p} regularity problem is equivalent to a weak reverse Hölder condition with exponent p.

Original language | English |
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Pages (from-to) | 1241-1264 |

Number of pages | 24 |

Journal | Transactions of the American Mathematical Society |

Volume | 363 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2011 |

## Keywords

- Dirichlet problem
- Lipschitz domains
- Regularity problem

## ASJC Scopus subject areas

- Mathematics (all)
- Applied Mathematics

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