Question: 1. (Schwarzs Reflection Principle) Let B + 1 = {(x, y) R 2 | x 2 + y 2 0} (1) and u C 2

1. (Schwarzs Reflection Principle) Let B + 1 = {(x, y) R 2 | x 2 + y 2 0} (1) and u C 2 (B + 1 ) C(B + 1 ), harmonic in B + 1 , u(x, 0) = 0. Show that the function U(x, y) = ( u(x, y), y 0 u(x, y), y

1. (Schwarzs Reflection Principle) Let B + 1 = {(x, y) R

1. (Schwarz's Reflection Principle) Let B; = {(x, y) R | z+? 0} and u E C? (B UCB;)), harmonie in B,1, u(7,0) = 0. Show that the function U (x, y) = 3 1) u(x, y), Y>0 (-u(x, -y), y

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