## Abstract

Let Ω be a bounded Lipschitz domain in ℝ^{n}, n ≥ 3. Let ω_{λ} (Q) = |Q - Q_{0}|^{λ}, where Q_{0} is a fixed point on ∂Ω. For a second order elliptic system with constant coefficients on Ω, we study boundary value problems with boundary data in the weighted space L^{2}(∂Ω, ω_{λ} d σ), where dσ denotes the surface measure on ∂Ω. We show that there exists ε > 0 such that the Dirichlet problem is uniquely solvable for - min(2+ε, n-1) < λ < ε, and the Neumann type problem is uniquely solvable if -ε < λ < min(2+ε, n-1). The regularity for the Dirichlet problem with data in the weighted Sobolev space L_{1}^{2}(∂Ω, ω_{λ} dσ) is also considered. Indiana University Mathematics Journal

Original language | English |
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Pages (from-to) | 1135-1154 |

Number of pages | 20 |

Journal | Indiana University Mathematics Journal |

Volume | 55 |

Issue number | 3 |

DOIs | |

State | Published - 2006 |

## Keywords

- Elliptic systems
- Lipschitz domains
- Weighted spaces

## ASJC Scopus subject areas

- Mathematics (all)