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Volume 39, Issue 2
The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations

Limei Dai

DOI: 10.4208/ata.OA-2022-0009

Anal. Theory Appl., 39 (2023), pp. 120-146.

Published online: 2023-06

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  • 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.

  • Keywords

Hessian equations, exterior Dirichlet problem, asymptotic behavior.

  • AMS Subject Headings

35J60, 35J25, 35B40, 35D40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-39-120, author = {Dai , Limei}, title = {The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {39}, number = {2}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2022-0009}, url = {http://global-sci.org/intro/article_detail/ata/21819.html} }
TY - JOUR T1 - The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations AU - Dai , Limei JO - Analysis in Theory and Applications VL - 2 SP - 120 EP - 146 PY - 2023 DA - 2023/06 SN - 39 DO - http://doi.org/10.4208/ata.OA-2022-0009 UR - https://global-sci.org/intro/article_detail/ata/21819.html KW - Hessian equations, exterior Dirichlet problem, asymptotic behavior. AB -

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.

Limei Dai. (2023). The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations. Analysis in Theory and Applications. 39 (2). 120-146. doi:10.4208/ata.OA-2022-0009
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