Problem detail · source-aware
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Lions asked whether the variational solution of a non-autonomous divergence-form problem has maximal L2-regularity under Holder continuity in time of the coefficients. Disproved at the half-Holder endpoint: a bounded, uniformly elliptic, real scalar coefficient, half-Holder in time and arbitrarily close to the heat equation, whose Lions solution has a time derivative that is not square integrable.
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The Declaration of AI Use: "During an exploratory analysis, a first counterexample was found by OpenAI's GPT-5.5 Pro in two dimensions and on the full space. It was then verified and studied by the author, who simplified it and reduced it to the one-dimensional interval counterexample presented here." GPT-5.6 Sol was separately used for drafting and revision of the exposition.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
A preprint days old, with no independent review.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Tensorisation and parabolic rescaling carry the one-dimensional example to real symmetric isotropic counterexamples on R^d and on every bounded domain, in every dimension.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.