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evinda

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I want to solve the Laplace equation on the unit disk, with boundary data $u(\theta)=\cos{\theta}$ on the unit circle $\{ r=1, 0 \leq \theta<2 \pi\}$. I also want to prove that little oscillations of the above boundary data give little oscillations of the corresponding solution of the Dirichlet problem after first stating strictly the statemtent.

How do we solve the Laplace equation on the unit disk with the given boundary data? Could you give me a hint? (Thinking)