Viscosity solutions of the augmented K-Hessian equations in exterior domains

  • Trong-Tien Phan
  • Hong-Quan g Dinh
  • Van-Bang Tran
Từ khóa: Augmented k-Hessian equations, viscosity solutions, subsolution, ( A, k)- convex function, exterior domain

Tóm tắt

This paper examines the Dirichlet problem for augmented -Hessian equations in exterior domains. Building upon our previous results on the viscosity solutions to the Dirichlet problems for augmented -Hessian equations in the bounded domain, and L. Dai, J. Bao's method to the -Hessian equations in exterior domains, a sufficient condition for the existence and uniqueness of viscosity solutions to the Dirichlet problem for the augmented -Hessian equations in exterior domains have been proven. During the process, a slight adjustment to the result on the existence and uniqueness of viscosity solutions to the problem in the bounded domains has been made for use in the present situation.

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Phát hành ngày
2024-08-30