2001/01/01 by Dorina Mitrea, Marius Mitrea, Michael E. Taylor · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Advanced Harmonic Analysis Research
paper · doi:10.1090/memo/0713
openalex publication_date 2001/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/21
Introduction Singular integrals on Lipschitz submanifolds of codimension one Estimates on fundamental solutions General second-order strongly elliptic systems The Dirichlet problem for the Hodge Laplacian and related operators Natural boundary problems for the Hodge Laplacian in Lipschitz domains Layer potential operators on Lipschitz domains Rellich type estimates for differential forms Fredholm properties of boundary integral operators on regular spaces Weak extensions of boundary derivative operators Localization arguments and the end of the proof of Theorem 6.2 Harmonic fields on Lipschitz domains The proofs of the Theorems 5.1-5.5 The proofs of the auxiliary lemmas Applications to Maxwell's equations on Lipschitz domains Analysis on Lipschitz manifolds The connection between d_∂ and d∂Ω Bibliography.