Prove the identity, where R is a simply connected region with boundary C. Assume that the required partial derivatives of the scalar functions ƒ and g are continuous. The expressions D_Nƒ and D_Ng are the derivatives in the direction of the outward normal vector N of C, and are defined by D_Nƒ = ∇ƒ ^. N, and D_Ng = ∇g ^. N.

Green’s second identity:

Transcribed Image Text:

SJ (fV²g - gv²f) dA = [ (fDng - gDNf) ds