The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations

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.

Author Details

Limei Dai