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## Due February 15

### Problem 1

Suppose $u$ is harmonic in a neighborhood of $\bar\Omega$, where $\Omega$ is a $C^1$ domain. Then
$\displaystyle \int_{\partial\Omega} \partial_\nu u \, d\sigma = 0$.

### Problem 2

If $\Omega\subset\mathbb R^d$ is a bounded domain and $u$ is harmonic in $\Omega$ and continuous on $\bar\Omega$, then $u$ takes its maximum and its minimum on $\partial\Omega$.

### Problem 3

Let $\Omega\subset\mathbb R^d$ be a bounded domain, $u$ and $v$ harmonic in $\Omega$ and continuous on $\bar\Omega$. If $u=v$ on $\partial\Omega$, then $u=v$ in $\Omega$.

### Problem 4

If $f$ is an entire function and its real part is nonnegative, then $f$ is constant.

### Problem 5

If $u$ is a radial harmonic function in $\mathbb B$, then it is constant.