  We establish higher-order weighted Sobolev and Holder regularity for
solutions to variational equations defined by the elliptic Heston operator, a
linear second-order degenerate-elliptic operator arising in mathematical
finance. Furthermore, given $C^\infty$-smooth data, we prove
$C^\infty$-regularity of solutions up to the portion of the boundary where the
operator is degenerate. In mathematical finance, solutions to obstacle problems
for the elliptic Heston operator correspond to value functions for perpetual
American-style options on the underlying asset.
