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Applications of Harmonic Functions — Howell & Matthews
Mathematics — Complex Analysis · dirichlet-problem-harmonic-functions
Problem Find the function ϕ ( x , y ) \phi(x,y) ϕ ( x , y ) x > 0 x > 0 x > 0 y > 0 y > 0 y > 0 ϕ ( 0 , y ) = 0 for y > 1 , ϕ ( 0 , y ) = 1 for 0 < y < 1 ; \phi(0,y) = 0 \text{ for } y > 1, \quad \phi(0,y) = 1 \text{ for } 0 < y < 1; ϕ ( 0 , y ) = 0 for y > 1 , ϕ ( 0 , y ) = 1 for 0 < y < 1 ; ϕ ( x , 0 ) = 1 for 0 ≤ x < 1 , ϕ ( x , 0 ) = 0 for x > 1. \phi(x,0) = 1 \text{ for } 0 \leq x < 1, \quad \phi(x,0) = 0 \text{ for } x > 1. ϕ ( x , 0 ) = 1 for 0 ≤ x < 1 , ϕ ( x , 0 ) = 0 for x > 1. Browse the problem library