A FREE BOUNDARY PROBLEM RELATED TO SINGLE-LAYER POTENTIALS
Peter Ebenfelt, Dmitry Khavinson, H. S. Shapiro · STIN · 2002
Let › be a bounded domain in R n with su-ciently regular boundary i , and let J be the operator which maps a function f on i to the restriction Jf to i of its single layer potential. In the present paper, we consider the problem of characterizing those domains › for which the constant function f · 1 is an eigenfunction for J and some related inverse problems. One of our main results concerning the former problem in R 2 » C is the following: If i is a rectiflable curve such that Cn › is a Smirnov domain and f· 1 is an eigenfunction for J , then i is a circle.