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arXiv · 2205.07200

The Dirichlet problem for Hessian quotient equations on exterior domains

Tangyu Jiang·Haigang Li·Xiaoliang Li
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Abstract

In this paper, we consider the exterior Dirichlet problem for Hessian quotient equations with the right hand side $g$, where $g$ is a positive function and $g=1+O(|x|^{-\beta})$ near infinity, for some $\beta>2$. Under a prescribed generalized symmetric asymptotic behavior at infinity, we establish an existence and uniqueness theorem for viscosity solutions, by using comparison principles and Perron's method. This extends the previous results for Monge--Amp\`ere equations and Hessian equations.

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Tangyu Jiang, Haigang Li, Xiaoliang Li. 2022-05-15. The Dirichlet problem for Hessian quotient equations on exterior domains. https://arxiv.org/abs/2205.07200

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