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Sharp Holder regularity for autonomous Beltrami equations
Abstract
Let Ω⊂ℂ be a domain and let ℋ:ℂ→ℂ be Lipschitz with constant 0<k<1. We prove that every weak W1,2loc solution of the autonomous Beltrami equation fz̅=ℋ(fz) belongs to C1,γloc, where γ=3/(2K+1) and K=(1+k)/(1−k). The exponent is optimal, resolving the conjecture of Astala, Clop, Faraco, Jääskeläinen and Koski.
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BibTeX
@misc{huang2026sharp,
title = {{Sharp Holder regularity for autonomous Beltrami equations}},
author = {Jie Huang and Jian-Feng Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25702},
eprint = {2610.25702},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25702},
}
RIS
TY - UNPB
TI - Sharp Holder regularity for autonomous Beltrami equations
AU - Jie Huang
AU - Jian-Feng Zhu
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25702
UR - https://arxiv.org/abs/2610.25702
AB - Let Ω⊂ℂ be a domain and let ℋ:ℂ→ℂ be Lipschitz with constant 0<k<1. We prove that every weak W^1,2_loc solution of the autonomous Beltrami equation f_z̅=ℋ(f_z) belongs to C^1,γ_loc, where γ=3/(2K+1) and K=(1+k)/(1−k). The exponent is optimal, resolving the conjecture of Astala, Clop, Faraco, Jääskeläinen and Koski.
ER -