OpenAI · 377-01 · 2026-10-04 · Partial differential equations
Uniform Interior C^{1,} Estimates for Infinity-Harmonic Functions
preprints/Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions-October-4-2026
Family 377. Interior regularity for infinity-harmonic functions.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves uniform interior regularity for bounded infinity-harmonic functions in every dimension , for a positive exponent depending only on dimension. The gradient's supremum norm and Hölder seminorm on the half unit ball are bounded by a dimension-dependent constant times the oscillation on the unit ball. The exponent is not explicit.
We prove a uniform interior estimate for bounded infinity-harmonic functions in every dimension d ≥ 3. For some depending only on the dimension, the gradient's supremum norm and αd-Hölder seminorm on B1/2 are bounded by a dimension-dependent constant times the oscillation on B1. The exponent is not explicit, and no endpoint or boundary regularity claim is made. In particular, infinity-harmonic functions are locally C1 on every open subset of ℝd, for d ≥ 3.
Preprint source and Lean scope
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