Year: 2026
Type: preprint
Abstract: We prove the $C^{p'}$-regularity conjecture in every dimension when $p>2$ is sufficiently close to $2$. To this end, we establish improved Hölder estimates for the gradients of $p$-harmonic functions. These estimates also determine the first-order asymptotics of the optimal gradient Hölder exponent in every dimension. The proof combines compactness, harmonic rigidity of the limiting profiles, and a sharp uniform gap estimate for the first variation of the gradient excess.
Source: arXiv (Cornell University)
Authors: Lee, Se-Chan, Lee, Taehun
Institution: Konkuk University
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212162601
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