On the general notion of fully nonlinear second-order elliptic equations

作者：Nicolai V. Krylov · 发表于：Transactions of the American Mathematical Society · 年份：1995 · DOI：10.1090/s0002-9947-1995-1284912-8 · 被引用次数：122 · 研究领域：Advanced Mathematical Physics Problems、Stability and Controllability of Differential Equations、Advanced Mathematical Modeling in Engineering

The general notion of fully nonlinear second-order elliptic equation is given. Its relation to so-called Bellman equations is investigated. A general existence theorem for the equations like ${P_m}({u_{{x^i}{x^j}}}) = \sum \nolimits _{k = 0}^{m - 1} {{c_k}(x){P_k}({u_{{x^i}{x^j}}})}$ is obtained as an example of an application of the general notion of fully nonlinear elliptic equations.