### Abstract

Let Ω ⊂ ℝ^{n} be a bounded domain, and let 1 < p < ∞ and σ < p. We study the nonlinear singular integral equation M[u](x) = f_{0}(x) in Ω with the boundary condition u = g_{0} on ∂Ω, where f_{0} ε C(Ω̄) and g_{0} ε C(∂Ω) are given functions and M is the singular integral operator given by, with some choice of ρ ε C(Ω̄) having the property, 0 < ρ(x) ≤ dist (x, ∂Ω). We establish the solvability (well-posedness) of this Dirichlet problem and the convergence uniform on Ω̄, as σ → p, of the solution u_{σ} of the Dirichlet problem to the solution u of the Dirichlet problem for the p-Laplace equation νΔ_{p}u = f_{0} in Ω with the Dirichlet condition u = g_{0} on ∂Ω, where the factor ν is a positive constant (see (7.2)).

Original language | English |
---|---|

Pages (from-to) | 485-522 |

Number of pages | 38 |

Journal | Calculus of Variations and Partial Differential Equations |

Volume | 37 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 2010 |

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

## Fingerprint Dive into the research topics of 'A class of integral equations and approximation of p-Laplace equations'. Together they form a unique fingerprint.

## Cite this

*Calculus of Variations and Partial Differential Equations*,

*37*(3-4), 485-522. https://doi.org/10.1007/s00526-009-0274-x