The Dirichlet Problems for a Class of Fully Nonlinear Elliptic Equations Relative to the Eigenvalues of the Hessian

Abstract

ln this paper we discuss the Dirichlet problems for a class of fully nonliucar elliptic equations F(D² u) = ψ(x, u)(ψ(x, u, ∇u)) \quad in Q u = φ(x) \quad on ∂Ω where F is represented by a symmetric function f(λ_1, …, λ_n) of the eigenvalues (λ_1, …,λ_n) of the Hessian D²u. This result extends the works of Caffarelli L., Nirenberg L., Spruck L. [2] to more general cases.