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Zero-normal-trace H(div) space

Definition

Assume Countable Choice for the Sobolev and weak normal trace interfaces. For an open set $D \subseteq R^{d}$ , let $T_{D} = H^{1} (D) / H_{0}^{1} (D)$ be the trace quotient of Weak normal trace by Green duality, and let $γ_{n} : H (div; D) \to T_{D}^{'}$ be its weak normal trace. Define

H_{0} (div; D) : = {v \in H (div; D) : γ_{n} v = 0 in T_{D}^{'}} .

Thus zero normal trace means that the Green-duality functional vanishes on every H1 trace class; no pointwise normal value is required.

Depends on

Used by

Dependency tree · two levels

11 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Daniele Boffi, Franco Brezzi and Michel Fortin, Mixed Finite Element Methods and Applications (standard reference, not scraped)
Jean-Luc Guermond, MATH 661 Fall 2025, Part III Chapter 14: H(div) finite elements (standard reference, not scraped)