P. Badiane

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20222025

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math.CV2025

Generalized study of the operator $α \partial^{k} \partial ˉ^{k} + β \partial ˉ^{k} + γ \partial^{k} + c$ in weighted Hilbert space $L^{2} (C, e^{- ∣ z ∣^{2}})$

Eramane Bodian, Winnie Ossete Ingoba, Souhaibou Sambou +2

By Hörmander's $L^{2}$ -method, we study the operator $α \partial^{k} \partial ˉ^{k} + β \partial ˉ^{k} + γ \partial^{k} + c$ for any order $k$ with $α, β, γ \in R$ such that $(…

math.CV2023

A variational approach to the eigenvalue problem for complex Hessian operators

Papa Badiane, Ahmed Zeriahi

Let $1 \leq m \leq n$ be two integers and $Ω\Subset \C^n$ a bounded $m$ -hyperconvex domain in $\C^n$. Using a variational approach, we prove the existence of the first eigenvalue a…

math.CV2023

The Eigenvalue Problem for the complex Monge-Ampère operator

Papa Badiane, Ahmed Zeriahi

We prove the existence of the first eigenvalue and an associated eigenfunction with Dirichlet condition for the complex Monge-Ampère operator on a bounded strongly pseudoconvex dom…

Generalized study of the operator α∂k∂ˉk+β∂ˉk+γ∂k+c in weighted Hilbert space L2(C,e−∣z∣2)

A variational approach to the eigenvalue problem for complex Hessian operators

The Eigenvalue Problem for the complex Monge-Ampère operator

Generalized study of the operator $α \partial^{k} \partial ˉ^{k} + β \partial ˉ^{k} + γ \partial^{k} + c$ in weighted Hilbert space $L^{2} (C, e^{- ∣ z ∣^{2}})$