Hessian商方程的外狄利克雷问题经典解的存在性
Existence of classical solutions to the exterior Dirichlet problem for Hessian quotient equations
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中文总结 AI 辅助
本文针对右端非恒定的Hessian商方程外狄利克雷问题，通过构造半径无关的边界到内部估计与爆破论证，证明了经典容许解的存在性及无穷远处Hessian的收敛性，还处理了源项非径向扰动等情形。
中文摘要 AI 辅助
本文研究右端项非恒定的Hessian商方程的外狄利克雷问题。我们证明了具有规定渐近Hessian的经典容许解的存在性，并建立了无穷远处Hessian的收敛性。主要难点在于在扩张的环带上获得关于外半径一致的二阶估计，以及在无规定衰减率的积分尾条件下推导Hessian收敛性，这些难点通过与半径无关的边界到内部估计和爆破论证得以解决。我们还允许源项的非径向扰动，在更强的点态假设下，我们获得了高阶渐近展开和对应任意足够大的规定渐近常数的解。
英文摘要
This paper studies the exterior Dirichlet problem for Hessian quotient equations with nonconstant right-hand sides. We prove the existence of classical admissible solutions with prescribed asymptotic Hessians and establish convergence of the Hessian at infinity. The main difficulties are obtaining second-order estimates on expanding annuli that are uniform in the outer radius and deriving Hessian convergence under an integral tail condition with no prescribed decay rate. These are resolved through a radius-independent boundary-to-interior estimate and a blow-down argument. We also allow nonradial perturbations of the source. Under stronger pointwise assumptions, we obtain higher-order asymptotic expansions and solutions for every sufficiently large prescribed asymptotic constant.
