On traces for H(curl,Ω) in Lipschitz domains

Fachrichtung 6 . 1 – Mathematik Preprint Nr . 323 Characterization of trace spaces of H ( curl , Ω ) on curvilinear Lipschitz polyhedral domains Ω

Finite Element Methods for Maxwell Equations

1. SOBOLEV SPACES AND WEAK FORMULATIONS Let Ω be a bounded Lipschitz domain in R. We introduce the Sobolev spaces H(curl ; Ω) = {v ∈ L(Ω), curlv ∈ L(Ω)}, H(div; Ω) = {v ∈ L(Ω),div v ∈ L(Ω)} The vector fields (E,H) belong to H(curl ; Ω) while the flux (D,B) in H(div; Ω). We shall use the unified notation H(d; Ω) with d = grad , curl , or div. Note that H(grad ; Ω) is the familiar H(Ω) space. The...

Mollification in Strongly Lipschitz Domains with Application to Continuous and Discrete De Rham Complex

We construct mollification operators in strongly Lipschitz domains that do not invoke non-trivial extensions, are Lp stable for any real number p ∈ [1,∞], and commute with the differential operators ∇, ∇×, and ∇·. We also construct mollification operators satisfying boundary conditions and use them to characterize the kernel of traces related to the tangential and normal trace of vector fields....

Mollification in Strongly Lipschitz Domains with Application to Continuous and Discrete De Rham Complexes

Weconstructmolli cation operators in strongly Lipschitz domains that do not invoke non-trivial extensions, are Lp stable for any real number p ∈ [1,∞], and commutewith thedi erential operators∇,∇×, and ∇⋅. We also constructmolli cation operators satisfying boundary conditions and use them to characterize the kernel of traces related to the tangential and normal trace of vector elds. We use the ...

Trace Theorems for Sobolev Spaces on Lipschitz Domains. Necessary Conditions

A famous theorem of E. Gagliardo gives the characterization of traces for Sobolev spaces W 1, p (Ω) for 1 ≤ p < ∞ when Ω ⊂ R is a Lipschitz domain. The extension of this result to W m, p (Ω) for m ≥ 2 and 1 < p < ∞ is now well-known when Ω is a smooth domain. The situation is more complicated for polygonal and polyhedral domains since the characterization is given only in terms of local compati...