OAI/Analysis/CircleDomains/Sobolev/PhysicalCoordinateLines.lean

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7 declarations, 0 contain sorry, 0 declared as axioms

Coordinate lines in the actual Euclidean Sobolev plane. Their one-dimensional derivatives and total energies are the physical partials.

  1. def OAI.CircleDomainRigidity.physicalCoordinateLine line 14
  2. theorem OAI.CircleDomainRigidity.physicalCoordinateLine_contDiff line 18
  3. theorem OAI.CircleDomainRigidity.physicalCoordinateLine_deriv line 23
  4. theorem OAI.CircleDomainRigidity.physicalCoordinateLine_energy_integrable line 41
  5. theorem OAI.CircleDomainRigidity.physicalCoordinateLine_energy_eq line 54
  6. theorem OAI.CircleDomainRigidity.physicalCoordinateLine_coordinate line 70
  7. theorem OAI.CircleDomainRigidity.physicalCoordinateLine_norm_le line 78