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The Dirichlet Problem of Hessian Equation in Exterior Domains

Author

Listed:
  • Hongfei Li

    (College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Limei Dai

    (School of Mathematics and Information Science, Weifang University, Weifang 261061, China)

Abstract

In this paper, we will obtain the existence of viscosity solutions to the exterior Dirichlet problem for Hessian equations with prescribed asymptotic behavior at infinity by the Perron’s method. This extends the Ju–Bao results on Monge–Ampère equations det D 2 u = f ( x ) .

Suggested Citation

  • Hongfei Li & Limei Dai, 2020. "The Dirichlet Problem of Hessian Equation in Exterior Domains," Mathematics, MDPI, vol. 8(5), pages 1-11, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:666-:d:351338
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    Cited by:

    1. Limei Dai & Xuewen Guo, 2022. "Parabolic Hessian Equations Outside a Cylinder," Mathematics, MDPI, vol. 10(16), pages 1-16, August.

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