OAI/MathematicalPhysics/ContinuumCoulomb/OneParticle/PlanarHeatDifferential.lean

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Pointwise differential identities for the actual two-dimensional Gaussian kernel. Its time derivative is its coordinate Laplacian.

  1. theorem OAI.ContinuumCoulomb.planarHeatKernel_C2 line 14
  2. def OAI.ContinuumCoulomb.planarHeatTimeDerivative line 18
  3. theorem OAI.ContinuumCoulomb.planarHeatKernel_hasDerivAt line 21
  4. theorem OAI.ContinuumCoulomb.planarHeatKernel_partial line 37
  5. theorem OAI.ContinuumCoulomb.planarHeatKernel_partial_partial line 49
  6. theorem OAI.ContinuumCoulomb.planarHeatKernel_laplacian line 73