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Failure of Interior Hölder and Gradient Estimates for the Subcritical Special Lagrangian Equation
Abstract
For every n≥3, we show, by a family of explicit entire real-analytic solutions, that, for every subcritical phase and every 0<α≤1, oscillation-based interior Cα estimates fail for the special Lagrangian equation in ℝn. In fact, this family has no common interior modulus of continuity.
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BibTeX
@misc{fan2026failure,
title = {{Failure of Interior Hölder and Gradient Estimates for the Subcritical Special Lagrangian Equation}},
author = {Zhenyu Fan and Caiyan Li and Zhehui Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01531},
eprint = {2609.01531},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01531},
}
RIS
TY - UNPB
TI - Failure of Interior Hölder and Gradient Estimates for the Subcritical Special Lagrangian Equation
AU - Zhenyu Fan
AU - Caiyan Li
AU - Zhehui Wang
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01531
UR - https://arxiv.org/abs/2609.01531
AB - For every n≥3, we show, by a family of explicit entire real-analytic solutions, that, for every subcritical phase and every 0<α≤1, oscillation-based interior C^α estimates fail for the special Lagrangian equation in ℝ^n. In fact, this family has no common interior modulus of continuity.
ER -