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The Landis conjecture on exponential decay

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arxiv 2007.07034 v1 pith:OVKFVEPF submitted 2020-07-14 math.AP math-phmath.CAmath.MP

A.Logunov , E.Malinnikova , N.Nadirashvili , F.Nazarov This is my paper · ORCID
classification math.APmath-phmath.CAmath.MP
keywords absoluteconjectureconsiderconstantdecaydeltaequivexponential
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abstract

Consider a solution $u$ to $\Delta u +Vu=0$ on $\mathbb{R}^2$, where $V$ is real-valued, measurable and $|V|\leq 1$. If $|u(x)| \leq \exp(-C |x| \log^{1/2}|x|)$, $|x|>2$, where $C$ is a sufficiently large absolute constant, then $u\equiv 0$.

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Cited by 2 Pith papers

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  1. Eigenfunctions with double exponential rate of localization

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    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.

  2. Elliptic regularity estimates with optimized constants and applications

    math.AP 2024-11 conditional novelty 7.0 of 10

    For divergence-form elliptic equations, the paper proves regularity estimates with constants exponential in a coefficient norm times domain radius, shows these exponents are optimal by explicit examples, and extends L...

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