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arXiv · 2208.03794

The exterior Dirichlet Problem for homogeneous complex $k$-Hessian equation

Zhenghuan Gao·Xi-Nan Ma·Dekai Zhang
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Abstract

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.

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Zhenghuan Gao, Xi-Nan Ma, Dekai Zhang. 2022-08-07. The exterior Dirichlet Problem for homogeneous complex $k$-Hessian equation. https://doi.org/10.1515/ans-2022-0039

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