| Abstract: |
| The Backus problem is the problem of finding a harmonic function on a given domain such that the modulus of its gradient coincides with prescribed values on the boundary of the domain. This problem appears when we try to determine the magnetic field of the Earth from the measurements of its intensity on the Earth`s surface. In this talk, we discuss the existence of solutions of the Backus problem in a neighborhood of a dipole, and observe that a solution is constructed if the given boundary values have symmetry. Deriving appropriate a priori estimates for the linearized problem around the dipole is the key to constructing the solution. |
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