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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

2 votes

Laplace equation with mixed boundary conditions

The solution to the Dirichlet problem is unique by the maximum principle. For the same reason, the solution to the Neumann problem is unique up to a constant. At worst your problem would fail uniquen …
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