The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations
Year: 2023
Author: Limei Dai
Analysis in Theory and Applications, Vol. 39 (2023), Iss. 2 : pp. 120–146
Abstract
In this paper, we consider the exterior Dirichlet problem of Hessian equations $$σ_k (λ(D^2u)) = g(x)$$ with $g$ being a perturbation of a general positive function at infinity. The existence of the viscosity solutions with generalized asymptotic behavior at infinity is established by the Perron’s method which extends the previous results for Hessian equations. By the solutions of Bernoulli ordinary differential equations, the viscosity subsolutions and supersolutions are constructed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2022-0009
Analysis in Theory and Applications, Vol. 39 (2023), Iss. 2 : pp. 120–146
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Hessian equations exterior Dirichlet problem asymptotic behavior.