## Abstract

Let Ω be a bounded Lipschitz domain in R^{n}. We develop a new approach to the invertibility on L^{p} (∂ Ω) of the layer potentials associated with elliptic equations and systems in Ω. As a consequence, for n ≥ 4 and frac(2 (n - 1), (n + 1)) - ε < p < 2 where ε > 0 depends on Ω, we obtain the solvability of the L^{p} Neumann type boundary value problems for second order elliptic systems. The analogous results for the biharmonic equation are also established.

Original language | English |
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Pages (from-to) | 212-254 |

Number of pages | 43 |

Journal | Advances in Mathematics |

Volume | 216 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 2007 |

### Bibliographical note

Funding Information:1 The author is supported in part by the NSF (DMS-0500257).

## Keywords

- Biharmonic equation
- Dirichlet problem
- Elliptic systems
- Lipschitz domains
- Neumann problem

## ASJC Scopus subject areas

- General Mathematics

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