OAI/MathematicalPhysics/DefocusingNLS/Profile/RadialSmoothBarrier.lean

GitHub source file

10 declarations, 0 contain sorry, 0 declared as axioms

Explicit twice differentiable barriers for the scalar inner problem.

  1. def OAI.DefocusingNLS.radialLowerBarrier line 10
  2. def OAI.DefocusingNLS.radialInverseBarrier line 13
  3. theorem OAI.DefocusingNLS.hasDerivAt_radialRamp_shift line 16
  4. theorem OAI.DefocusingNLS.hasDerivAt_radialRampD_shift line 21
  5. theorem OAI.DefocusingNLS.hasDerivAt_radialLowerBarrier line 26
  6. theorem OAI.DefocusingNLS.radialLowerBarrier_laplacian line 31
  7. theorem OAI.DefocusingNLS.hasDerivAt_radialInverseBarrier line 42
  8. theorem OAI.DefocusingNLS.radialInverseBarrier_laplacian line 46
  9. theorem OAI.DefocusingNLS.radialInverseBarrier_boundary line 57
  10. theorem OAI.DefocusingNLS.radialInverseBarrier_bounds line 61