Source-pinned research

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 187 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.30.0

Wkp U deriv ELp Norm zero le e Norm

WkpU.derivELpNorm_zero_le_eNorm

Plain-language statement

The eLpNorm of f is bounded by the Sobolev eNorm.

partial differential equationsSobolev spacesanalysis

Source project: PDE

Person-level attribution pending.

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Project-declaredLean 4.30.0

Wkp U deriv To Lp sub

WkpU.derivToLp_sub

Plain-language statement

The projection of the weak derivative of f - g to Lp equals the difference of the projections of the weak derivatives of f and g.

partial differential equationsSobolev spacesanalysis

Source project: PDE

Person-level attribution pending.

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Project-declaredLean 4.30.0

Wkp U e Norm add le

WkpU.eNorm_add_le

Plain-language statement

Triangle inequality for eLpNorm.

partial differential equationsSobolev spacesanalysis

Source project: PDE

Person-level attribution pending.

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Project-declaredLean 4.30.0

Wkp U e Norm eq zero of ae zero

WkpU.eNorm_eq_zero_of_ae_zero

Plain-language statement

If f : WkpU d k p U hU is almost everywhere zero on U, then its Sobolev eNorm is zero.

partial differential equationsSobolev spacesanalysis

Source project: PDE

Person-level attribution pending.

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Project-declaredLean 4.30.0

Wkp U e Norm ne top

WkpU.eNorm_ne_top

Plain-language statement

The W^{k,p}(U) norm is finite.

partial differential equationsSobolev spacesanalysis

Source project: PDE

Person-level attribution pending.

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Project-declaredLean 4.30.0

Wkp U e Norm smul

WkpU.eNorm_smul

Plain-language statement

Absolute homogeneity for eNorm .

partial differential equationsSobolev spacesanalysis

Source project: PDE

Person-level attribution pending.

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