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

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.