Viscosity solutions of the augmented K-Hessian equations


  • Van - Bang Tran Hanoi Pedagogical University 2, 32 Nguyen Van Linh, Phuc Yen, Vinh Phuc, Vietnam
  • Tien-Ngoan Ha Institute of Mathematics, Vietnam Academy of Science and Technology
  • Huu-Tho Nguyen Thuyloi University
  • Trong-Tien Phan Quang Binh University
  • Lan-Huong Nguyen T78 Friendship School



In this paper, the Dirichlet problem for the augmented k – Hessian equations in the bounded domain with nonsmooth data will be investigated. We introduce the concept of (w,k) – convex function, show that all viscosity subsolutions and supersolutions of the considering Dirichlet problem are (w,k) – convex. Furthermore, we prove some sufficient conditions for the existence and uniqueness of the viscosity solutions of the Dirichlet problem


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How to Cite

Tran, V. .-. B., Ha, T.-N., Nguyen, H.-T., Phan , T.-T., & Nguyen, L.-H. (2022). Viscosity solutions of the augmented K-Hessian equations. HPU2 Journal of Science: Natural Sciences and Technology, 1(1), 3–9.

Volume and Issue


Natural Sciences and Technology