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Kinetic Trace Estimates in the Gaussian Model

Differential equations · posed by Dallas Albritton, Scott Armstrong, Jean-Christophe Mourrat, Matthew Novack, 2024 · disproved

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Statement

Does the natural trace estimate hold for kinetic energy spaces in the unrestricted Gaussian velocity model on bounded domains (Question 1.8 of Albritton, Armstrong, Mourrat and Novack)? No: for each 1≤p<21 \le p < 2 there are counterexamples on every bounded C1,1\mathrm{C}^{1,1} domain in dimension d≥2d \ge 2. The paper also identifies the sharp boundary-regularity threshold C1,1/2\mathrm{C}^{1,1/2} for the natural trace weight.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Lukas Niebel and Lisa Valentini, using GPT-5.5 Pro, GPT-5.6 Sol

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    GPT-5.5 Pro provided preliminary counterexamples and GPT-5.6 Sol an initial proof of the natural half-space trace estimate; generative AI was also used in developing some of the subsequent arguments. The authors developed and verified the final theory.

    the named open question is answered negatively; the paper's positive theory goes further

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