Volume 5, Issue 2
The Dirichlet Problems for a Class of Fully Nonlinear Elliptic Equations Relative to the Eigenvalues of the Hessian

Wang Lianju

J. Part. Diff. Eq.,5(1992),pp.53-68

Published online: 1992-05

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  • 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.

  • Keywords

The eigenvalues of the Hessian matrix admissible a priori estimates for the C&sup2 norm

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@Article{JPDE-5-53, author = {Wang Lianju}, title = {The Dirichlet Problems for a Class of Fully Nonlinear Elliptic Equations Relative to the Eigenvalues of the Hessian}, journal = {Journal of Partial Differential Equations}, year = {1992}, volume = {5}, number = {2}, pages = {53--68}, 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5737.html} }
TY - JOUR T1 - The Dirichlet Problems for a Class of Fully Nonlinear Elliptic Equations Relative to the Eigenvalues of the Hessian AU - Wang Lianju JO - Journal of Partial Differential Equations VL - 2 SP - 53 EP - 68 PY - 1992 DA - 1992/05 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5737.html KW - The eigenvalues of the Hessian matrix KW - admissible KW - a priori estimates for the C² norm AB - 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.
Wang Lianju. (1970). The Dirichlet Problems for a Class of Fully Nonlinear Elliptic Equations Relative to the Eigenvalues of the Hessian. Journal of Partial Differential Equations. 5 (2). 53-68. doi:
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