Elliptic Solutions to Nonsymmetric Monge-Ampère Type Equations II. A Priori Estimates and the Dirichlet Problem

Ngoan, Ha Tien; Chung, Thai Thi Kim

doi:10.1007/s40306-018-0270-3

Cited by 3 publications

(2 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…x , we have 4), ( 6) and (7). If the equation in (3) has a viscosity subsolution 1 v and a viscosity supersolution 2 v being locally Lipschitz on  , 12 vv == on  then, there exists a unique viscosity solution of the problem (3).…”

Section: Definition 11 ([1]mentioning

confidence: 99%

“…If the data of the problem are sufficiently smooth, classical solutions of Dirichlet problems for Monge-Ampere equations have been studied, even for a more general class of equations in [7], [8]. Meanwhile, classical solutions to (1)-( 2) have been investigated in [5] and further extended for oblique boundary value problems for the augmented Hessian equations in [6].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Viscosity solutions of the augmented K- Hessian equations

Tran,

Ha,

Nguyen

et al. 2022

HPU2: JS

View full text Add to dashboard Cite

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

show abstract

Section: Definition 11 ([1]mentioning

confidence: 99%

mentioning

confidence: 99%