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**Term Test 2 / TT2--Problem 5**

« **on:**November 15, 2012, 08:26:34 PM »

Let $Q = \{(x,y)\in {\mathbb{R}}^2: |x|<1, |y|<1\}.$ Draw the set $Q.$ We define data $g$ on the boundary of $Q$:

Find the solution $u$ of the Dirichlet problem on $Q$:

\begin{equation*}

\Delta u=0 \qquad \text{for } (x,y) \in Q

\end{equation*}

with the boundary conditions

\begin{equation*}

u = \left\{\begin{aligned}

&y &&\text{as }x=1,\\[3pt]

-&y &&\text{as }x=-1,\\[3pt]

&x &&\text{as }y=1,\\[3pt]

-&x &&\text{as }y=-1.

\end{aligned}\right.

\end{equation*}

Post after 22:30

Find the solution $u$ of the Dirichlet problem on $Q$:

\begin{equation*}

\Delta u=0 \qquad \text{for } (x,y) \in Q

\end{equation*}

with the boundary conditions

\begin{equation*}

u = \left\{\begin{aligned}

&y &&\text{as }x=1,\\[3pt]

-&y &&\text{as }x=-1,\\[3pt]

&x &&\text{as }y=1,\\[3pt]

-&x &&\text{as }y=-1.

\end{aligned}\right.

\end{equation*}

Post after 22:30