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Applications of Harmonic Functions — Howell & Matthews
Mathematics — Complex Analysis · dirichlet-problem-quarter-disk
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 ∣ z ∣ < 1 |z| < 1 ∣ z ∣ < 1 ϕ ( x , y ) = 3 for x + i y = z = e i θ , 0 < θ < π 2 ; \phi(x,y) = 3 \text{ for } x + iy = z = e^{i\theta},\; 0 < \theta < \frac{\pi}{2}; ϕ ( x , y ) = 3 for x + i y = z = e i θ , 0 < θ < 2 π ; ϕ ( x , 0 ) = − 3 for 0 ≤ x < 1 ; \phi(x,0) = -3 \text{ for } 0 \leq x < 1; ϕ ( x , 0 ) = − 3 for 0 ≤ x < 1 ; ϕ ( 0 , y ) = − 3 for 0 < y < 1. \phi(0,y) = -3 \text{ for } 0 < y < 1. ϕ ( 0 , y ) = − 3 for 0 < y < 1. Browse the problem library