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For questions regarding harmonic functions.
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Boundary regularity for the Dirichlet problem
Let us consider the unit ball $B^n$ of $\mathbf{R}^n$ and $K = B^{n-1}(0,1/2) \times \{0\}$ the ball of dimension $n-1$ and radius $1/2$ lying on the equator.
We wish to solve the Dirichlet problem ( …