Failure of Interior Hölder and Gradient Estimates for the Subcritical Special Lagrangian Equation

Abstract

For every $n\ge 3$, we show, by a family of explicit entire real-analytic solutions, that, for every subcritical phase and every $0<\alpha \le 1$, 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.

8 pages, comments are welcome