Alexander Ramm
Mathematics Department, Kansas State University, Manhattan, KS 66506
On symmetry problems
Suppose that S, a smooth surface homeomorphic to a sphere,
is the boundary of a domain D, and the overdetermined problem
(L+k^2) u = 0 in
D, u = 1 on
S and u_N = 0 on
S has a solution. Does it follow that
S is a sphere? This is a problem equivalent to the
Pompeiu problem. Other problems of this type are considered.