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arXiv · 1607.07194

Concavity of the Lagrangian Phase Operator and Applications

Tristan C. Collins·Sebastien Picard·Xuan Wu
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Abstract

We study the Dirichlet problem for the Lagrangian phase operator, in both the real and complex setting. Our main result states that if $\Omega$ is a compact domain in $\mathbb{R}^{n}$ or $\mathbb{C}^n$, then there exists a solution to the Dirichlet problem with right-hand side $h(x)$ satisfying $|h(x)| > (n-2)\frac{\pi}{2}$ and boundary data $\phi$ if and only if there exists a subsolution.

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Tristan C. Collins, Sebastien Picard, Xuan Wu. 2016-07-25. Concavity of the Lagrangian Phase Operator and Applications. https://arxiv.org/abs/1607.07194

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