| Abstract: |
| Bernoulli`s free boundary problem is an overdetermined boundary value problem in which one seeks an annular domain with a fixed exterior boundary and an interior free boundary, such that the associated capacitary potential also satisfies a prescribed Neumann boundary condition on the free boundary.
I will talk about recent developments regarding to a conjecture of Flucher and Rumpf that asserts the existence of a family of free boundaries concentrating at non-degenerate local minima of the Robin function. |
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