Lions' Maximal Regularity Problem at the Half-Holder Endpoint
Statement
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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No person has examined this. Nothing here has been checked at all. say whether it holds →
construction · #1
GPT-5.5 Pro, with Lukas NiebelThe record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.
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.
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