A note on the Schiffer conjecture
Robert Dalmasso · Hokkaido Mathematical Journal · 1999
A domain \Omega\subset \mathbb{R}^{n}(n\geq 2) with smooth connected boundary is said to have the Schiffer property if there is no \lambda>0 such that the overdetermined boundary value problem \triangle u+\lambda u+1=0 in \Omega , u= \frac{\partial u}{\partial u}=0 on \partial\Omega where u is the exterior normal to \partial\Omega , has a solution.We prove integral identities for the exterior normal to the boundary of a domain \Omega lacking the Schiffer property.