clopen.solutions

Failure of comparison for a relaxed infinity fractional evolution

Recorded by the registry's curators from GitHub; the authors did not submit it here.

Kaiwen Jin

We consider the infinity fractional evolution in dimension $n\ge2$, with $1/2<s<1$. At a zero spatial test gradient, the viscosity subsolution condition uses the supremum of symmetric directional integrals, and the supersolution condition uses their infimum. For this convention, comparison fails even for radial subsolutions and supersolutions with the same compactly supported initial data, attained uniformly. The construction uses two thin annuli: a line tangent to the inner annulus collects substantially more mass than a radial line. This permits a locally flat subsolution to rise faster than a radial solution of the one-dimensional fractional heat equation.

Claims

SOLUTION CLAIMED OP-00800 — Comparison for viscosity solutions of infinity-fractional diffusion
Counterexample · fidelity not yet established

Files and sources

Paper
AIM @ 24edaad, 461-relaxed-infinity-fractional-comparison/paper.pdf ↗
Posted on GitHub
15 October 2026

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