Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 377-01. Uniform Interior C (1,α) Estimates for Infinity-Harmonic Functions
Manuscript map · lines 9625–9634
OpenAI@2026-10-07#rem:oai-p-377-01
Authors: OpenAI. Family 377.
Title: Uniform Interior $C{}{1,{}alpha}$ Estimates for Infinity-Harmonic Functions.
Abstract: We prove a uniform interior $C{}{1,{}alpha_d}$ estimate for bounded infinity-harmonic functions in every dimension d ≥ 3. For some ${}alpha_d{}in(0,1/3]$ 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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