Abstract: | In this paper we present and analyze two new algorithms
to construct a smooth diffeomorphism of a domain with prescribed
jacobian function. The first one is free from any restriction on
the boundary, while the second one produces a diffeomorphism that
coincides with the identity map on the boundary of the domain.
Both are based on the solution of an initial value problem for the
linear heat equation, and the second also uses solutions of the
Stokes system of Fluid Mechanics. |