Three harmonic functions u, k = 1, 2, 3 are defined on the domain CR, k...

 

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Three harmonic functions u, k = 1, 2, 3 are defined on the domain CR², k = 1,2,3 given as follows. Particularly, ₁ is a disk of radius 1, ₂ is a square of side length 2, and 3 is an equilateral triangle of side length 2. F (b) ₂ (a) ₁ (c) N3 On the boundary each function u, takes two values, 0 or 1. As indicated in the graph above, u(x, y) = 0 for all (x, y) on the dashed portion, whereas u(x, y) = 1 for all (x, y) on the solid portion. (a) Which k € {1,2,3} has the largest value u(x, yk), where (x, y) is the (rotational) center of the domain ? (b) Which k € {1,2,3} has the largest integral ff u(x,y)dady? Three harmonic functions u, k = 1, 2, 3 are defined on the domain CR², k = 1,2,3 given as follows. Particularly, ₁ is a disk of radius 1, ₂ is a square of side length 2, and 3 is an equilateral triangle of side length 2. F (b) ₂ (a) ₁ (c) N3 On the boundary each function u, takes two values, 0 or 1. As indicated in the graph above, u(x, y) = 0 for all (x, y) on the dashed portion, whereas u(x, y) = 1 for all (x, y) on the solid portion. (a) Which k € {1,2,3} has the largest value u(x, yk), where (x, y) is the (rotational) center of the domain ? (b) Which k € {1,2,3} has the largest integral ff u(x,y)dady?

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ANSWER a k 3 has the largest value at the center of the domain b k 1 has the largest in... View the full answer