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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 2007 • Question 7

Question

Math 6420 • PDE Fall 2007 • Question 7

Solve Laplace’s equation \(\Delta \phi =0\) in the domain between the two nonconcentric circles \(|z|=1\) and \(|z-1|=5/2\), subject to the boundary conditions \(\phi =a\) on \(|z|=1\) and \(\phi =b\) on \(|z-1|=5/2\).

Raw LaTeX

Solve Laplace's equation \(\Delta\phi=0\) in the domain between the two nonconcentric circles
\(|z|=1\) and \(|z-1|=5/2\), subject to the boundary conditions \(\phi=a\) on \(|z|=1\) and
\(\phi=b\) on \(|z-1|=5/2\).

Topic Tags

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