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Research proof index

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 2,569 curated research declarations and 119,070 complete package declarations. Search 10,000 more complete Mathlib declarations.

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Showing 817 to 822 of 2,569 results.

Project-declaredLean 4.29.0-rc6

Moser Reg Power Cutoff Witness norm sq le

DeGiorgi.moserRegPowerCutoffWitness_norm_sq_le

Project documentation

Pointwise gradient norm bound for the regularized powered cutoff. Extracted as a standalone lemma to keep the surrounding proof context small.

partial differential equationsregularity theoryanalysis

Source project: DeGiorgi

Person-level attribution pending.

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Project-declaredLean 4.29.0-rc6

Moser Reg Test Cutoff mem H01

DeGiorgi.moserRegTestCutoff_memH01

Mathematical statement

The regularized Moser test function belongs to H₀¹(B_s).

partial differential equationsregularity theoryanalysis

Source project: DeGiorgi

Person-level attribution pending.

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Project-declaredLean 4.29.0-rc6

Moser Reg Test Pow nonneg of nonneg

DeGiorgi.moserRegTestPow_nonneg_of_nonneg

Mathematical statement

The moserRegTestPow is nonneg on nonneg inputs: since smoothClip(t) ≥ 0 for t ≥ 0, we have (ε + smoothClip(t))^{p-1} ≥ ε^{p-1}.

partial differential equationsregularity theoryanalysis

Source project: DeGiorgi

Person-level attribution pending.

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Project-declaredLean 4.29.0-rc6

Norm smooth Fun To Lp eq

DeGiorgi.norm_smoothFunToLp_eq

Mathematical statement

Norm of the class carried by a smooth test function.

partial differential equationsregularity theoryanalysis

Source project: DeGiorgi

Person-level attribution pending.

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Project-declaredLean 4.29.0-rc6

Rescale To Unit Ball is Homogeneous Weak Solution

DeGiorgi.rescaleToUnitBall_isHomogeneousWeakSolution

Mathematical statement

Transport homogeneous weak solutions on B(x₀, R) to the unit ball via affine pullback.

partial differential equationsregularity theoryanalysis

Source project: DeGiorgi

Person-level attribution pending.

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Project-declaredLean 4.29.0-rc6

Rescale To Unit Ball is Subsolution

DeGiorgi.rescaleToUnitBall_isSubsolution

Mathematical statement

Transport subsolutions on B(x₀, R) to the unit ball via affine pullback.

partial differential equationsregularity theoryanalysis

Source project: DeGiorgi

Person-level attribution pending.

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