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Landis' conjecture: a survey

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arxiv 2412.00788 v2 pith:GUIMLPPE submitted 2024-12-01 math.AP

Aingeru Fernández-Bertolin , Diana Stan , Luz Roncal This is my paper · ORCID
classification math.AP
keywords conjecturesurveyaccountadvancescloselycomplementconnectedcontexts
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We survey Kondrat'ev--Landis' conjecture, providing an up-to-date account of the main advances and describing the techniques developed. We complement the overview with references and formulations of the problem in further closely connected contexts.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Counterexamples to the Landis conjecture in dimensions three and higher

    math.AP 2026-08 accept novelty 8.0 of 10

    For every n≥3, the authors construct a nonzero real smooth solution u of -Δu+V u=0 with bounded real V and |u(x)|≤C exp(-c|x|^{4/3}), giving a counterexample to the Landis conjecture in that setting.

  2. A Rellich-type theorem for the Helmholtz equation in a junction of stratified media

    math.AP 2025-04 accept novelty 7.0 of 10

    No nonzero L2 solution of the Helmholtz equation exists in a 2D junction of three stratified half-planes with branch angles at least pi/2; hence no trapped modes there.

  3. On Support Cardinality for the Discrete Schr\"odinger Equation

    math-ph 2026-06 unverdicted novelty 6.0 of 10

    Minimal support cardinality S_d(N) of nontrivial origin-nonzero Dirichlet solutions is nondecreasing in d, so S_4(N) ≳ N²/log N, matching even-dimensional constructions up to a log factor.

  4. An optimal fractional Hardy inequality on the discrete half-line

    math.AP 2025-07 conditional novelty 6.0 of 10

    For σ in (0,1], the paper constructs an explicit optimal Hardy weight W^op_σ for (-Δ_N)^σ, with W^op_σ(n) approximately n^{-2σ} and an upper bound C_σ for the best constant in the n^{-2σ} Hardy inequality.

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