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arXiv · 2609.01531

Failure of Interior H\"older and Gradient Estimates for the Subcritical Special Lagrangian Equation

Zhenyu Fan·Caiyan Li·Zhehui Wang
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Abstract

For every $n\ge3$, we show, by a family of explicit entire real-analytic solutions, that, for every subcritical phase and every $0<\alpha\le1$, oscillation-based interior $C^\alpha$ estimates fail for the special Lagrangian equation in $\mathbb{R}^n$. In fact, this family has no common interior modulus of continuity.

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Zhenyu Fan, Caiyan Li, Zhehui Wang. 2026-09-01. Failure of Interior H\"older and Gradient Estimates for the Subcritical Special Lagrangian Equation. https://arxiv.org/abs/2609.01531

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