Connor Mooney, Ovidiu Savin
Published 2018-06-14Version 1
We study the equation $u_{11}u_{22} = 1$ in $\mathbb{R}^2$. Our results include an interior $C^2$ estimate, classical solvability of the Dirichlet problem, and the existence of non-quadratic entire solutions. We also construct global singular solutions to the analogous equation in higher dimensions. At the end we state some open questions.
Applications of Fourier analysis in homogenization of Dirichlet problem II. $L^p$ estimates
Dirichlet problems on graphs with ends
The Dirichlet problem for nonlocal operators with singular kernels: convex and nonconvex domains
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