For each integer d≥3 there are αd∈(0,1/3] and Cd<∞ such that every bounded infinity-harmonic function on the unit ball has gradient supremum and αd-Hölder seminorm on the half ball bounded by Cd times its oscillation on the unit ball.
For each integer d≥3 there are αd∈(0,1/3] and Cd<∞ such that every bounded infinity-harmonic function on the unit ball has gradient supremum and αd-Hölder seminorm on the half ball bounded by Cd times its oscillation on the unit ball.
For each integer d≥3 there are αd∈(0,1/3] and Cd<∞ such that every bounded infinity-harmonic function on the unit ball has gradient supremum and αd-Hölder seminorm on the half ball bounded by Cd times its oscillation on the unit ball.
If correct, upgrades pointwise differentiability to uniform local C¹,α regularity in every higher dimension.
Do infinity-harmonic functions in dimensions at least three have uniform interior Hölder-continuous gradients?
Publication dates and editorial changes.
OpenAI reports uniform interior C¹,α bounds for infinity-harmonic functions
Allow optional Google Analytics to help improve AIProofWatch? Privacy details.
