Zeitschrift für angewandte Mathematik und Physik ZAMP

, Volume 54, Issue 6, pp 919–936

On maps with given Jacobians involving the heat equation

  • Albert Avinyó
  • Joan Solà-Morales
  • Marta València
Original paper

DOI: 10.1007/s00033-003-0070-y

Cite this article as:
Avinyó, A., Solà-Morales, J. & València, M. Z. angew. Math. Phys. (2003) 54: 919. doi:10.1007/s00033-003-0070-y

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.

Mathematics Subject Classification (2000):

35J6035B65

Keywords.

Prescribed jacobian equationHölder regularityHeat equationStokes system

Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  • Albert Avinyó
    • 1
  • Joan Solà-Morales
    • 2
  • Marta València
    • 3
  1. 1.Departament de Matemàtica Aplicada 2, Universitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Departament de Matemàtica Aplicada 1, Universitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Departament de Matemàtica Aplicada 1, Universitat Politècnica de CatalunyaBarcelonaSpain