Alphabeta Math
DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generated
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.

Small-strain elasticity with a frictionless contact gap

Definition

Use the polygon, displacement space and oriented contact normal from Partial-trace displacement space on a polygon. Let the constant shear modulus satisfy μ>0, let the finite Lam'e parameter satisfy λ≥0, and let F:V→R be a bounded linear functional. For v∈V, define the weak symmetric gradient ε(v):=∇v+(∇v)T2. For u,v∈V, define the isotropic small-strain elasticity form a(u,v):=∫Ω2μ ε(u):ε(v)+λ div⁡u div⁡v dx. The strain and form conventions are the algebraic formulas in Linear isotropic elasticity: displacement form and data. The present domain is the partial-trace space V; all coercivity and well-posedness claims for it are proved locally below.

Depends on

Used by

Dependency tree · two levels

8 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