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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2006 • Question 7

Question

Math 6420 • PDE Fall 2006 • Question 7

Solve the Laplace equation \(\Delta \phi =0\) subject to the boundary conditions: \[ \begin {aligned} \phi& =a &&\text {on } \{z: |z|=2,\ z\ne 2\},\\ \phi& =b &&\text {on } \{z: |z-1|=1,\ z\ne 2\}. \end {aligned} \] (\(a\) and \(b\) are real constants; \(z=x+iy\).)

Raw LaTeX

Solve the Laplace equation \(\Delta\phi=0\) subject to the boundary conditions:
\[
\begin{aligned}
\phi&=a &&\text{on } \{z: |z|=2,\ z\ne 2\},\\
\phi&=b &&\text{on } \{z: |z-1|=1,\ z\ne 2\}.
\end{aligned}
\]
(\(a\) and \(b\) are real constants; \(z=x+iy\).)

Topic Tags

Distributions and Weak Solutions Fundamental Solutions Laplace Equation Linear Programming and Optimization