Green's second identity

⌠ ⌡ ⌠ ⌡ Ω  (u ∆v − v ∆u) dS = ⌠ (⎜) ⌡ ∂Ω  ⎛ ⎝ u ∂v ∂n − v ∂u ∂n ⎞ ⎠ dl.

From the first Green's identity,

⌠ ⌡ V  (∇u ·∇v + u ∇2 v) dV = ⌠ (⎜) ⌡ S  u ∂v ∂n dS, (1) ⌠ ⌡ V  (∇v ·∇u + v ∇2 u) dV = ⌠ (⎜) ⌡ S  v ∂u ∂n dS. (2)

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File translated from T_EX by T_TH, version 4.03.
On 21 Aug 2022, 22:51.