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Uniqueness and radial symmetry for an inverse elliptic equation. (English) Zbl 1130.35332

Summary: 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.

MSC:

35J35 Variational methods for higher-order elliptic equations
35J60 Nonlinear elliptic equations
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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