Source-pinned research
Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.
This index contains 2 research declarations. Search 10,000 more complete Mathlib declarations.
2 results
Clear filtersDeGiorgi.log_gradient_bound_eps
Plain-language statement
Regularized logarithmic gradient bound: for fixed ε > 0, ∫_Ω φ²|∇u|²/(u+ε)² ≤ 4Λ ∫_Ω |∇φ|². This is the ε-level estimate that feeds into log_gradient_bound_of_supersolution via ε → 0.
Source project: DeGiorgi
Person-level attribution pending.
DeGiorgi.log_gradient_bound_of_supersolution
Plain-language statement
Logarithmic gradient bound for positive supersolutions. If u > 0 satisfies -∇·(A∇u) ≥ 0 on Ω, then for every smooth cutoff φ supported in Ω: ∫_Ω φ² |∇u|²/u² ≤ 4Λ ∫_Ω |∇φ|². Equivalently, setting v = -log u: ∫_Ω φ² |∇v|² ≤ 4Λ ∫_Ω |∇φ|². Proof: apply log_gradient_bound_eps for each ε > 0 to get ∫ φ²|∇u|²/(u+ε)² ≤ 4Λ ∫ |∇φ|², then send...
Source project: DeGiorgi
Person-level attribution pending.