The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian

@article{Caffarelli1985TheDP,
  title={The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian},
  author={Luis Caffarelli and Louis Nirenberg and Joel Spruck},
  journal={Acta Mathematica},
  year={1985},
  volume={155},
  pages={261-301}
}
On etudie le probleme de Dirichlet dans un domaine borne Ω de R n a frontiere lisse ∂Ω:F(D 2 u)=ψ dans Ω, u=φ sur ∂Ω 
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References

SHOWING 1-10 OF 14 REFERENCES
The dirichlet problem for nonlinear second‐order elliptic equations. II. Complex monge‐ampère, and uniformaly elliptic, equations
On considere le probleme de Dirichlet pour des equations elliptiques non lineaires d'ordre 2 pour une fonction reelle dans un domaine borne Ω de R n a frontiere lisse ∂Ω
ON DEGENERATE NONLINEAR ELLIPTIC EQUATIONS
Dirichlet problems for degenerate nonlinear elliptic equations of Bellman type are studied, where is a linear elliptic operator of second order. Under certain conditions on the coefficients of , it
THE INTEGRAL METHOD OF BARRIER FUNCTIONS AND THE DIRICHLET PROBLEM FOR EQUATIONS WITH OPERATORS OF MONGE-AMPÈRE TYPE
A priori boundedness of the solution of the Dirichlet problem is proved for the equation , where is the sum of all principal minors of order in the Hessian . The boundedness in question is relative
BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS IN A DOMAIN
In this paper the Dirichlet problem is studied for equations of the form and also the first boundary value problem for equations of the form , where and are positive homogeneous functions of the
On the regularity of the solution of the n‐dimensional Minkowski problem
where xi are the coordinate functions on S". Minkowski then asked the converse of the problem. Namely, given a positive function K defined on S" satisfying the above integral conditions, can we find
The Dirichlet problem for nonlinear second-order elliptic equations I
A green tire carrier having a wheeled frame providing support at three levels thereof for tire carrying sling members, each sling member being adjustable between several operative positions and an
An Inequality for Hyperbolic Polynomials
Improper afine hyperspheres of convex rype and a generalizarion of a theorem by K . Jiirgens , Michigan Math
  • 1958
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