Work

Hessian quotient equations on exterior domains

Year: 2025

Type: article

Abstract: It is well-known that a celebrated Jörgens-Calabi-Pogorelov theorem for Monge-Ampère equations states that any classical (viscosity) convex solution of $ \det(D^2u) = 1 $ in $ \mathbb{R}^n $ must be a quadratic polynomial. Therefore, it is an interesting topic to study the existence and uniqueness theorem of such fully nonlinear partial differential equations' Dirichlet problems on exterior domains with suitable asymptotic conditions at infinity. As a continuation of the works of Caffarelli-Li for Monge-Ampère equation and of Bao-Li-Li for $ k $-Hessian equations, this paper is devoted to the solvability of the exterior Dirichlet problem of Hessian quotient equations $ \sigma_k(\lambda(D^2u))/\sigma_l(\lambda(D^2u)) = 1 $ for any $ 1\leq l

Source: Communications on Analysis and Computation

DOI: 10.3934/cac.2025009

Authors: Haigang Li, Xiaoliang Li, Shuyang Zhao

Institutions: Beijing Normal University, Peking University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Awards: G4312569926, G5384318372