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