On the exterior Dirichlet problem for Hessian equations
Jiguang Bao, Haigang Li, Yanyan Li
TL;DR
This paper proves the existence of solutions with specific behavior at infinity for the exterior Dirichlet problem related to Hessian equations, extending previous results from Monge-Ampère equations.
Contribution
It generalizes the existence theorem from Monge-Ampère equations to a broader class of Hessian equations for exterior boundary conditions.
Findings
Existence of solutions with prescribed asymptotic behavior
Extension of Caffarelli and Li's result to Hessian equations
Theoretical proof of solution existence
Abstract
In this paper, we establish a theorem on the existence of the solutions of the exterior Dirichlet problem for Hessian equations with prescribed asymptotic behavior at infinity. This extends a result of Caffarelli and Li for the Monge-Amp\`{e}re equation to Hessian equations.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations