Abstract
We consider an overdetermined problem associated to an inhomogeneous
infinity-Laplace equation. More precisely, the domain of the problem
is required to contain a given compact set K of positive reach, and
the boundary of the domain must lie within the reach of K. We look
for a solution vanishing at the boundary and such that the outer
derivative depends only on the distance from K. We prove that if the
boundary gradient grows fast enough with respect to such distance
(faster than the distance raised to
{\frac{1}{3}}
), then the problem is
solvable if and only if the domain is a tubular neighborhood of K,
thus extending a previous result valid in the case when K is made up
of a single point.