| Abstract: |
| The equation $(u_{11}u_{22})^{1/2} = 1$ in $\mathbb{R}^2$ is a simple example of a concave, fully nonlinear elliptic PDE that is not a Hessian equation. It shares interesting features with the complex Monge-Ampere equation, such as non-convexity of solutions and invariance under adding certain quadratics. We will present some regularity results for this equation and its higher-dimensional analogue, as well as open problems. This is joint work with O. Savin. |
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