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

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References

  1. [1]

    Caffarelli, L., Nirenberg, L. &Spruck, J., The Dirichlet problem for nonlinear second order elliptic equations, I: Monge-Ampère equations.Comm. Pure Appl. Math. 37 (1984), 369–402.

    MathSciNet  Google Scholar 

  2. [2]

    Caffarelli, L., Kohn, J. J., Nirenberg, L. &Spruck, J.. The Dirichlet problem for nonlinear second order elliptic equations, II: Complex Monge-Ampère, and uniformly elliptic equations.Comm. Pure Appl. Math., 38 (1985), 209–252.

    MathSciNet  Google Scholar 

  3. [3]

    Gårding, L., An inequality for hyperbolic polynomials.J. Math. Mech., 8 (1959), 957–965.

    MATH  MathSciNet  Google Scholar 

  4. [4]

    Harvey, R. &Lawson jr, H. B., Calibrated geometries.Acta Math., 148 (1982), 47–157.

    MathSciNet  Google Scholar 

  5. [5]

    Ivočkina, N. M., The integral method of barrier functions and the Dirichlet problem for equations with operators of Monge-Ampère type.Mat. Sb. (N.S.), 112 (1980), 193–206 (Russian);Math. USSR-Sb., 40 (1981), 179–192 (English).

    MathSciNet  Google Scholar 

  6. [6]

    Krylov, N. V., Boundedly inhomogeneous elliptic and parabolic equations in a domain.Izv. Akad. Nauk SSSR, 47 (1983), 75–108.

    MATH  MathSciNet  Google Scholar 

  7. [7]

    Marcus, M., An eigenvalue inequality for the product of normal matrices.Amer. Math. Monthly, 63 (1956), 173–174.

    Article  MATH  MathSciNet  Google Scholar 

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Dedicated to Lars Gårding on his 65th birthday

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Caffarelli, L., Nirenberg, L. & Spruck, J. The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian. Acta Math. 155, 261–301 (1985). https://doi.org/10.1007/BF02392544

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Keywords

  • Elliptic Equation
  • Dirichlet Problem
  • Order Elliptic Equation