## Question

###### 5) Let D {0 < I < y 1} and be harmonic in D with the boundary conditions u(r, 0) 12 u(z.1) 12 _ 1, "(0,y) ~y} , u(1,y) = 1 y? a) What is the maximum ankl minimum values of u in D? Assume that U 15 another harmonic function On the entire plane with v(0,0) = 1. Can v be zero for all values (I.y) outside of some disc?

5) Let D {0 < I < y 1} and be harmonic in D with the boundary conditions u(r, 0) 12 u(z.1) 12 _ 1, "(0,y) ~y} , u(1,y) = 1 y? a) What is the maximum ankl minimum values of u in D? Assume that U 15 another harmonic function On the entire plane with v(0,0) = 1. Can v be zero for all values (I.y) outside of some disc?

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