International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 48, Pages 3047-3052
doi:10.1155/S0161171203211236

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

Abstract

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.