Uniqueness and radial symmetry for an inverse elliptic equation - B. Emamizadeh; M. H. Mehrabi (International Journal of Mathematics and Mathematical Sciences)
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.