For homogeneous fully nonlinear elliptic equations with injective DF, the DN map determines the source uniquely after the second linearization removes the conformal factor under an algebraic nondegeneracy condition.
Calder\'on problem for the quasilinear conductivity equation in dimension 2
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An inverse source problem for a fully nonlinear elliptic equation
For homogeneous fully nonlinear elliptic equations with injective DF, the DN map determines the source uniquely after the second linearization removes the conformal factor under an algebraic nondegeneracy condition.