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Where g(u,v) is obtained from f(x,y) by substitution, using the equations (3) We will derive the formula (5) for the new area element in the next section;'%%( # IZ Vb^an cVbZ 8gnhdXadg^YVZ gZZgh cdi id jg Xdadjg!V so that LK = IW and KL = IVThen for any y = IW(y) = L(K(y)) so we can let x = K(y), which means L is onto If L(x1) = L(x2) then x1 = IV (x1) = KL(x1) = KL(x2) = IV (x2) = x2, which means L is 1¡1

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The NPUX June meeting will be conducted remotely To register in advance, click here Meeting ID 940 6017 9815 DialIn , access code, # NPUY Agenda Third Monday 700 pm John Birdine Facility 215 Lakewood Way Atlanta, GA The NPUY June meeting will be conducted remotely To register in advance, click HEREWhere Φ is the fundamental solution of Laplace's equation and for each x 2 Ω, hx is a solution of (45) We leave it as an exercise to verify that G(x;y) satisfies (42) in the sense of distributions Conclusion If u is a (smooth) solution of (41) and G(x;y) is the Green's function for ΩW and K W !

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