A real scalar 1/2-Hölder coefficient arbitrarily close to 1 can destroy maximal L2-regularity for divergence-form parabolic equations, confirming the Auscher-Egert conjecture.
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Lions' Maximal Regularity Problem for Divergence-Form Differential Operators: Failure at the $\frac{1}{2}$-H\"older Endpoint
A real scalar 1/2-Hölder coefficient arbitrarily close to 1 can destroy maximal L2-regularity for divergence-form parabolic equations, confirming the Auscher-Egert conjecture.