{"id":"openai-math/Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions","pdf":"https://github.com/openai/math/blob/main/preprints/Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions-October-4-2026/interior-c1-infinity-harmonic.pdf","url":"https://github.com/openai/math/tree/main/preprints/Uniform-Interior-C1alpha-Estimates-for-Infinity-Harmonic-Functions-October-4-2026","tags":["pde","infinity-harmonic","regularity"],"score":0,"title":"Uniform Interior $`C^{1,\\alpha}`$ Estimates for Infinity-Harmonic Functions","domain":"Partial differential equations","family":"377","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AP","summary":"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 α d -Hölder seminorm on B 1/2 are bounded by a dimension-dependent constant times the oscillation on B 1 . The exponent is not explicit, and no endpoint or boundary regularity claim is made. In particular, infinity-harmonic functions are locally C 1 on every open subset of ℝ d , for d ≥ 3.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-04","reactions":{},"formalized":false,"family_title":"Interior $`C^{1,\\alpha}`$ regularity for infinity-harmonic functions"}