If two active scalar equations with fractional dissipation produce the same observations on a small open set, their nonlocal drift operators must agree on the whole exterior, according to the paper's main theorem.
The higher order fractional Calder´ on problem for linear local operators: Uniqueness
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A Calder\'on type inverse problem for the active scalar equations with fractional dissipation
If two active scalar equations with fractional dissipation produce the same observations on a small open set, their nonlocal drift operators must agree on the whole exterior, according to the paper's main theorem.