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Dokumententyp
Institution
Spezialsammlung
Sprache
- Englisch (1)
Autor
- Hiptmair, Ralf (1)
- Kotiuga, Peter (1)
- Tordeux, Sébastien (1)
Fachgebiet
Schlagwort
- $${C^{\infty}_{0}(D)}$$ : Compactly supported functions in C ∞(D), $${{\rm {\bf C}}_{0}^{\infty}(D)=(C^{\infty}_{0}(D))^{3}}$$ (1)
- $${HF^{-\frac{1}{2},k}({\mathsf{d}}, {\partial}{D})}$$ : Trace space of $${HF^{k}({\mathsf{d}},D)}$$ (1)
- $${HF^{\frac{3}{2},0}({\partial}{D})}$$ : See (5.5) (1)
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$${HF^{k}({\mathsf{d}},D)}$$ : Square integrable k-forms with square integrable exterior derivative (1)
- $${HF^{k}_{0}({\mathsf{d}},D)}$$ : Completion of compactly supported k-forms in $${HF^{k}({\mathsf{d}},D)}$$ (1)
- $${HZ^{-\frac{1}{2},k}({\partial}{D})}$$ : Closed k-forms in $${{HF^{-\frac{1}{2},1}({\mathsf{d}}, {\partial}{D})}}$$ , see for instance (6.1) (1)
- $${H^{\frac{1}{2}} (\partial{D})}$$ : Trace space of $${H^1(D):=\{u\in {L^2(D)}:\nabla {u} \in {L^2(D)}\}}$$ (1)
- $${H{\frac{3}{2}}(\partial{D})}$$ : See (5.3) (1)
- $${S_i,S^{\prime}_{i}}$$ : Inside and outside cuts of D, see Sect. 6.3 (1)
- $${\langle\cdot\rangle}$$ : (Relative) Homology class of a cycle (1)
- $${\mathbf{H}^{-\frac{1}{2}}_{\mathbf{t}}({\rm curl}_\partial, \partial{D})}$$ : Tangential traces of vector fields in H(curl, D) (1)
- $${\mathbf{H}^{s}_{\mathbf{t}}(\partial{D}),\mathbf{L}^{2}_{\mathbf{t}}(\partial{D})}$$ : Tangential trace spaces (1)
- $${\mathsf{T},\mathsf{T}*}$$ : An (unbounded) linear operator and its adjoint (1)
- $${\mathsf{T}_{min}}$$ , $${\mathsf{T}_{s}}, \mathsf{T}_{max}$$ : Min, self-adj. and max closures of a symmetric operator $${\mathsf{T}}$$ (1)
- $${\omega,\eta,\ldots}$$ : Differential forms (1)
- $${\omega^{0},\omega^{\perp}}$$ : Components of the Hodge decomposition of $${\omega \in {HF^{-\frac{1}{2},1}}{(\mathsf{d},{\partial}{D})}}$$ (1)
- $${\star}$$ $$({\star_{g}})$$ : Hodge operator (induced by metric g) (1)
- $${\wedge}$$ : Exterior product of differential forms (1)
- $${{L}^{\sharp}}$$ : Symplectic orthogonal of subspace L of a symplectic space (1)
- $${{\bf grad}_\partial}$$ : Surface gradient (1)
- $${{\mathcal D}(\mathsf{T})}$$ : Domain of definition of the linear operator $${\mathsf{T}}$$ (1)
- $${{\mathcal H}^{1}({\partial}{D})}$$ : Co-homology space of harmonic 1-forms on $${{\partial}{D}}$$ (1)
- $${{\mathcal N}({\mathsf{T}})}$$ : Kernel (null space) of linear operator $${\mathsf{T}}$$ (1)
- $${{\mathcal R}({\mathsf{T}})}$$ : Range space of a linear operator $${\mathsf{T}}$$ (1)
- $${{\mathsf{d}}}$$ : Exterior derivative of differential forms (1)
- $${{\partial}{M}}$$ : Boundary of M (1)
- $${{\rm curl}_{\partial}}$$ : Scalar valued surface rotation (1)
- $${{\rm div}_\partial}$$ : Surface divergence (1)
- $${{\rm {\bf u}},{\rm {\bf v}}, \ldots}$$ : Vector fields on a three-dimensional domain or elements of trace space of vector proxies (1)
- (·, ·) : Inner product: for $${\omega\in L^{2}(\Lambda^{k}(M))}$$ , $${(\omega,\omega)_{k,M}=\int_{M}\omega\wedge\star\omega}$$ (1) Mehr Weniger