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On maps with given Jacobians involving the heat equation |
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| Authors: | Email author&prev_q=Albert?Avinyó |
| Institution: | (1) Departament de Matemàtica Aplicada 2, Universitat Politècnica de Catalunya, C. Pau Gargallo, 5, 08028 Barcelona, Spain;(2) Departament de Matemàtica Aplicada 1, Universitat Politècnica de Catalunya, Av. Diagonal, 647, 08028 Barcelona, Spain;(3) Departament de Matemàtica Aplicada 1, Universitat Politècnica de Catalunya, Av. Diagonal, 647, 08028 Barcelona, Spain |
| 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. |
| Keywords: | 35J60 35B65 |
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