DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-09

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Classical normal derivative

Definition

For a bounded $C^{1}$ domain $Ω$ and $u \in C^{1} (\overline{Ω})$ , the classical normal derivative is $\partial_{ν} u (x) = D u (x) \cdot ν (x)$ on $\partial Ω$ . Here Du is the continuous extension of the interior gradient and $ν$ is the outward unit normal. For a specified finite piecewise $C^{1}$ presentation define the same expression on each face off its edge set E; arbitrary values on E do not change a surface integral. This definition uses a classical continuous trace, and asserts neither a Sobolev trace nor a conormal derivative.

Source notes

Hunter §2.5, immediately before Theorem 2.23, printed p. 32 (PDF p. 38).

Depends on

Used by

First Green identity Corollary

Dependency tree · two levels

6 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

Hunter, Notes on Partial Differential Equations (standard reference, not scraped)