Nonzero eigenfunctions and A-harmonic functions of uniformly elliptic C1-coefficient operators, plus a complex-valued heat-equation solution, can achieve the maximal allowed double-exponential decay in cylinders.
Davey,Some Quantitative Unique Continuation Results for Eigenfunctions of the Magnetic Schr¨ odinger Operator, Communi- cations in partial differential equations39 (2014), no
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Eigenfunctions with double exponential rate of localization
Nonzero eigenfunctions and A-harmonic functions of uniformly elliptic C1-coefficient operators, plus a complex-valued heat-equation solution, can achieve the maximal allowed double-exponential decay in cylinders.