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Optimal unique continuation for periodic elliptic equations on large scales

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arxiv 2107.14248 v1 pith:PAEKKOL3 submitted 2021-07-29 math.AP

Scott Armstrong , Tuomo Kuusi , Charles Smart This is my paper · ORCID
classification math.AP
keywords optimaldoublingellipticequationsinequalitylarge-scaleperiodicalmost
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We prove a quantitative, large-scale doubling inequality and large-scale three-ellipsoid inequality for solutions of uniformly elliptic equations with periodic coefficients. These estimates are optimal in terms of the minimal length scale on which they are valid, and are at least "almost" optimal in the prefactor constants--up to, at most, an iterated logarithm of the initial doubling ratio.

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  1. Eigenfunctions with double exponential rate of localization

    math.AP 2025-01 conditional novelty 7.0 of 10

    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.

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