Viscosity solutions to complex first eigenvalue equations

Soufian Abja

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arXiv · 2104.05484

Viscosity solutions to complex first eigenvalue equations

Soufian Abja

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Abstract

We study the viscosity solutions to the first eigenvalue equation. We consider $\Omega$ a bounded B-regular domain in $\mathbb{C}^n$ and we prove that the Dirichlet problem $\Lambda_{1}(D_{\mathbb{C}}^2 u)=f$ in $\Omega$ and $u=\varphi$ on $\partial\Omega$ admits a unique viscosity solution. We also deal with viscosity theory for operators which are comparable to the first eigenvalue operator.

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Soufian Abja. 2021-04-12. Viscosity solutions to complex first eigenvalue equations. https://arxiv.org/abs/2104.05484

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