OAI/Analysis/HotSpots/Trace.lean

GitHub source file

50 declarations, 0 contain sorry, 0 declared as axioms

  1. lemma OAI.StrictHotSpots.Nodal.transition_deriv_zero line 13
  2. def OAI.StrictHotSpots.Nodal.cutoff line 25
  3. lemma OAI.StrictHotSpots.Nodal.cutoff_contDiff line 27
  4. lemma OAI.StrictHotSpots.Nodal.cutoff_deriv line 31
  5. lemma OAI.StrictHotSpots.Nodal.cutoff_zero line 43
  6. lemma OAI.StrictHotSpots.Nodal.cutoff_norm_le line 50
  7. lemma OAI.StrictHotSpots.Nodal.cutoff_deriv_bound line 55
  8. lemma OAI.StrictHotSpots.Nodal.cutoff_eventually_eq line 80
  9. def OAI.StrictHotSpots.BoundarySign.cut line 100
  10. def OAI.StrictHotSpots.BoundarySign.cutSupport line 102
  11. lemma OAI.StrictHotSpots.BoundarySign.support_cut_subset line 104
  12. lemma OAI.StrictHotSpots.BoundarySign.cutSupport_closed line 112
  13. lemma OAI.StrictHotSpots.BoundarySign.cutSupport_subset line 115
  14. lemma OAI.StrictHotSpots.BoundarySign.cut_eq_zero_nhds line 124
  15. lemma OAI.StrictHotSpots.BoundarySign.cut_eq_nhds line 129
  16. lemma OAI.StrictHotSpots.BoundarySign.cut_contDiff line 133
  17. lemma OAI.StrictHotSpots.BoundarySign.cut_tsupport_subset line 143
  18. lemma OAI.StrictHotSpots.BoundarySign.cut_hasCompactSupport line 147
  19. def OAI.StrictHotSpots.BoundarySign.test line 153
  20. lemma OAI.StrictHotSpots.BoundarySign.cut_gradient line 158
  21. lemma OAI.StrictHotSpots.BoundarySign.gap_test line 168
  22. lemma OAI.StrictHotSpots.BoundarySign.equation_test line 194
  23. lemma OAI.StrictHotSpots.Nodal.cutoff_nonpos line 216
  24. lemma OAI.StrictHotSpots.Nodal.cutoff_deriv_nonpos line 218
  25. lemma OAI.StrictHotSpots.Nodal.cutoff_tendsto line 224
  26. lemma OAI.StrictHotSpots.Nodal.cutoff_deriv_tendsto line 230
  27. lemma OAI.StrictHotSpots.Nodal.cutoff_square_integral line 238
  28. lemma OAI.StrictHotSpots.Nodal.cutoff_product_integral line 252
  29. lemma OAI.StrictHotSpots.Nodal.cutoff_deriv_integral line 270
  30. lemma OAI.StrictHotSpots.Nodal.cutoff_deriv_square_integral line 286
  31. lemma OAI.StrictHotSpots.Nodal.cutoff_indicator_zero_nhds line 314
  32. lemma OAI.StrictHotSpots.Nodal.cutoff_indicator_contDiffOn line 328
  33. lemma OAI.StrictHotSpots.Nodal.cutoff_indicator_fderiv line 339
  34. lemma OAI.StrictHotSpots.Nodal.cutoff_indicator_gradient line 355
  35. lemma OAI.StrictHotSpots.Nodal.cutoff_memLp line 367
  36. lemma OAI.StrictHotSpots.Nodal.cutoff_grad_memLp line 376
  37. lemma OAI.StrictHotSpots.Nodal.cutoff_hasH1Gradient line 391
  38. lemma OAI.StrictHotSpots.Nodal.hasH1Gradient_indicator line 413
  39. lemma OAI.StrictHotSpots.Nodal.positive_set_open line 468
  40. lemma OAI.StrictHotSpots.Nodal.positive_component_frontier_zero line 472
  41. lemma OAI.StrictHotSpots.Nodal.positive_component_hasH1Gradient line 503
  42. lemma OAI.StrictHotSpots.positive_region_frontier_zero line 520
  43. lemma OAI.StrictHotSpots.positive_part_gradient line 534
  44. lemma OAI.StrictHotSpots.positive_part_memH10 line 542
  45. theorem OAI.StrictHotSpots.smooth_zero_trace_memH10 line 584
  46. lemma OAI.StrictHotSpots.BoundarySign.cut_contDiff_interior line 625
  47. def OAI.StrictHotSpots.BoundarySign.test_interior line 635
  48. lemma OAI.StrictHotSpots.BoundarySign.cut_gradient_interior line 640
  49. lemma OAI.StrictHotSpots.positive_part_memH10_interior line 651
  50. theorem OAI.StrictHotSpots.interior_smooth_zero_trace_memH10 line 690