### Abstract

Given a bounded Lipschitz domain Ω ⊂ ℝ^{n} n ≥ 3, we prove that the Poisson's problem for the Laplacian with right-hand side in L_{-t}^{p}(Ω), Robin-type boundary datum in the Besov space B_{p}^{1-1/p-t,p}(∂Ω) and non-negative, non-everywhere vanishing Robin coefficient b ∈ L ^{n-1}(∂ω), is uniquely solvable in the class L _{2-t}^{p}(Omega;) for (t, 1/p) ∈ ν_{ε}, where ν_{ε} (ε ≥ 0) is an open (Ω,b)-dependent plane region and ν_{0} is to be interpreted ad the common (optimal) solvability region for all Lipschitz domains. We prove a similar regularity result for the Poisson's problem for the 3-dimensional Lamé System with traction-type Robin boundary condition. All solutions are expressed as boundary layer potentials.

Original language | English (US) |
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Pages (from-to) | 181-204 |

Number of pages | 24 |

Journal | Revista Matematica Iberoamericana |

Volume | 22 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2006 |

Externally published | Yes |

### Keywords

- Besov spaces
- Boundary layer potentials
- Lamé system
- Non-smooth domains
- Poisson's problem
- Regularity of PDE's
- Robin condition
- TYiebel-Lizorkin spaces

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*Revista Matematica Iberoamericana*,

*22*(1), 181-204. https://doi.org/10.4171/RMI/453