OAI/MathematicalPhysics/DefocusingNLS/Profile/CartesianDirectionalCalculus.lean

GitHub source file

9 declarations, 0 contain sorry, 0 declared as axioms

Constant Cartesian derivatives commute with each other and the Laplacian.

  1. def OAI.DefocusingNLS.cartesianDerivative line 12
  2. theorem OAI.DefocusingNLS.cartesianDerivative_contDiff line 15
  3. theorem OAI.DefocusingNLS.cartesianDerivative_second line 19
  4. theorem OAI.DefocusingNLS.cartesianDerivative_commute line 28
  5. theorem OAI.DefocusingNLS.cartesianDerivative_sum line 35
  6. theorem OAI.DefocusingNLS.laplacian_eq_cartesianDerivatives line 44
  7. theorem OAI.DefocusingNLS.laplacian_cartesianDerivative line 55
  8. theorem OAI.DefocusingNLS.laplacian_contDiff line 70
  9. theorem OAI.DefocusingNLS.cartesianDerivative_transport line 76