Proof of the Schiffer's conjecture

A. G. Ramm

The following conjecture has been known for many decades as Schiffer's symmetry problem (or Schiffer's conjecture): Assume that $\Delta u+k^{2}u=0$ in $D$, $u{|}_S=0$, $u_N{|}_S=1$, where $D\s…