The exterior Dirichlet Problem for homogeneous complex \(k\)-Hessian equation

The exterior Dirichlet Problem for homogeneous complex \(k\)-Hessian equation

In this paper, we consider the homogeneous complex k-Hessian equation in an exterior domain \(\mathbb{C}^n\setminus\Omega\). We prove the existence and uniqueness of the \(C^{1,1}\) solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate a...

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Veröffentlicht in:arXiv.org 2022-08
Hauptverfasser: Gao, Zhenghuan, Xi-Nan Ma, Zhang, Dekai
Format: Artikel
Sprache:eng
Schlagworte:
Dirichlet problem
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Zusammenfassung:In this paper, we consider the homogeneous complex k-Hessian equation in an exterior domain \(\mathbb{C}^n\setminus\Omega\). We prove the existence and uniqueness of the \(C^{1,1}\) solution by constructing approximating solutions. The key point for us is to establish the uniform gradient estimate and the second order estimate.
ISSN:2331-8422
DOI:10.48550/arxiv.2208.03794