\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Entire solutions with asymptotic behavior of fully nonlinear uniformly elliptic equations

Abstract / Introduction Related Papers Cited by
  • In this paper, we use the Perron method to prove the existence of viscosity solutions with asymptotic behavior at infinity to fully nonlinear uniformly elliptic equations in $R^n$.
    Mathematics Subject Classification: Primary: 35J60.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    J. G. Bao, Fully nonlinear elliptic equations on general domains, Canad. J. Math., 54 (2002), 1121-1141.doi: 10.4153/CJM-2002-042-9.

    [2]

    Luis A. Caffarelli and X. Cabré, "Fully Nonlinear Elliptic Equations," Colloquium Publications, 43, American Mathematical Society, Providence, RI, 1995.

    [3]

    X. Cabré and Luis A. Caffarelli, Regularity for viscosity solutions of fully nonlinear equations $F(D^2u)=0$, Topol. Methods Nonlinear Anal., 6 (1995), 31-48.

    [4]

    L. Caffarelli and Y. Y. Li, An extension to a theorem of Jörgens, Calabi, and Pogorelov, Comm. Pure Appl. Math., 56 (2003), 549-583.doi: 10.1002/cpa.10067.

    [5]

    L. M. Dai and J. G. BaoEntire solutions with asymptotic behavior of Hessian equations, Adv. Math. (China), in press.

    [6]

    Lawrence C. Evans, Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math., 35 (1982), 333-363.doi: 10.1002/cpa.3160350303.

    [7]

    D. Gilbarg and Neil S. Trudinger, "Elliptic Partial Differential Equations of Second Order," 2nd edition, Springer-Verlag, Berlin, 1983.

    [8]

    H. Ishii, On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDEs, Comm. Pure Appl. Math., 42 (1989), 15-45.doi: 10.1002/cpa.3160420103.

    [9]

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

    [10]

    O. Savin, Entire solutions to a class of fully nonlinear elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci., 7 (2008), 369-405.

    [11]

    B. Sirakov, Solvability of uniformly elliptic fully nonlinear PDE, Arch. Ration. Mech. Anal., 195 (2010), 579-607.doi: 10.1007/s00205-009-0218-9.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(65) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return