OAI/Geometry/EinsteinFour/ScalarAdjointCoordinates.lean

GitHub source file

11 declarations, 0 contain sorry, 0 declared as axioms

The density-weighted chart equation gives the formal adjoint of the nondivergence operator. Its expansion has the same principal coefficients, a differentiated drift, and an explicit smooth zeroth-order potential.

  1. def OAI.PositiveEinsteinFour.Geometry.scalarFormalAdjointOperator line 22
  2. def OAI.PositiveEinsteinFour.Geometry.scalarAdjointDrift line 27
  3. def OAI.PositiveEinsteinFour.Geometry.scalarAdjointPotential line 30
  4. theorem OAI.PositiveEinsteinFour.Geometry.scalar_adjoint_multiplier_sum line 33
  5. theorem OAI.PositiveEinsteinFour.Geometry.scalar_adjoint_multiplier_add line 43
  6. theorem OAI.PositiveEinsteinFour.Geometry.scalar_adjoint_multiplier_sub line 48
  7. theorem OAI.PositiveEinsteinFour.Geometry.scalarAdjoint_second_product line 53
  8. theorem OAI.PositiveEinsteinFour.Geometry.scalarFormalAdjointOperator_expansion line 70
  9. theorem OAI.PositiveEinsteinFour.Geometry.scalar_adjoint_nine_bound line 90
  10. theorem OAI.PositiveEinsteinFour.Geometry.scalarAdjointDrift_bound line 109
  11. theorem OAI.PositiveEinsteinFour.Geometry.scalarAdjointDrift_derivative_bound line 117