On maps with given jacobians involving the heat equation
2000
In this paper we presennt 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.
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