I am trying to solve the following:

If $g$ is bounded and $g(x)=|x|$ for $x\in \mathbb{R}^{n-1}$ such that $|x|\leq 1$, then $Du$ is unbounded in a neighboorhood of zero.

Remembering that: the problem is $$ \left\{\begin{array}{ll} \Delta u = 0 , \ in \ \mathbb{R}_{+}^{n} \\ u=g , \ in \ \mathbb{R}^{n-1} \end{array}\right. $$ and $u(x)=\int\limits_{\mathbb{R}^{n-1}}\dfrac{2x_{n}}{n\omega_{n}|x-y|^{n}}g(y)dS_{y}$.

I would be gratefull if some can give me some help.


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