International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 48, Pages 3047-3052

Uniqueness and radial symmetry for an inverse elliptic equation

B. Emamizadeh1,2 and M. H. Mehrabi1

1Department of Mathematics, Iran University of Science and Technology, Tehran 16844, Narmak, Iran
2Institute for Studies in Theoretical Physics and Mathematics, Niavaran Square, Tehran, Iran

Received 7 November 2002

Copyright © 2003 B. Emamizadeh and M. H. Mehrabi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider an inverse rearrangement semilinear partial differential equation in a 2-dimensional ball and show that it has a unique maximizing energy solution. The solution represents a confined steady flow containing a vortex and passing over a seamount. Our approach is based on a rearrangement variational principle extensively developed by G. R. Burton.