## f-extremal disk

In the last nonlinear analysis seminar, Professor Espinar talked about the overdetermined elliptic problem(OEP) which looks like the following

There is a BCN conjecture related to this

**BCN: **If is Lipschitz, is a smooth(in fact, Lipschitz) connected domain with connected where OEP admits a bounded solution, then must be either a ball, a half space, a generalized cylinder or the complement of one of them.

BCN is false in . Epsinar wih Mazet proved BCN when . This implies the Shiffer conjecture in dimension 2. In higher dimension of Shiffer conjecture, if we know the domain is contained in one hemisphere of , then one can use the equator or the great circle to perform the moving plane.

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