The Dirichlet problem for nonsymmetric augmented k-Hessian type equations

To solve the Dirichlet problem for nonsymmetric augmented k-Hessian type equations, 2≤k≤n, we first of all solve this problem for corresponding symmetric augmented k-Hessian type ones. Then, by using the Banach fixed point theorem, we prove the existence of δ-admissible solution in C2,α of the probl...

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Bibliographic Details
Published in:Nonlinear analysis 2025-02, Vol.251, p.113684, Article 113684
Main Authors: Tran, Bang Van, Ha, Ngoan Tien, Nguyen, Tho Huu, Phan, Tien Trong
Format: Article
Language:English
Subjects:
Admissible solution
Nonsymmetric augmented k-Hessian type equation
δ-admissible solution
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Summary:To solve the Dirichlet problem for nonsymmetric augmented k-Hessian type equations, 2≤k≤n, we first of all solve this problem for corresponding symmetric augmented k-Hessian type ones. Then, by using the Banach fixed point theorem, we prove the existence of δ-admissible solution in C2,α of the problem, provided that the skew-symmetric matrices entering the equations are sufficiently small in some sense. Some necessary conditions for existence and sufficient conditions for uniqueness of this kind of solution are given.
ISSN:0362-546X
DOI:10.1016/j.na.2024.113684