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Complex Variables and Elliptic Equations
An International Journal
Volume 62, 2017 - Issue 8
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Original Articles

Hessian measures on m-polar sets and applications to the complex Hessian equations

Vu Viet HungDepartment of Mathematics, Physics and Informatics, Tay Bac University, .Correspondence[email protected]
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Nguyen Van PhuPostgraduate Department, Hanoi Electric Power University, Hanoi, Vietnam.View further author information
Pages 1135-1164 | Received 01 Jun 2016, Accepted 11 Dec 2016, Published online: 14 Feb 2017

References

  • Bedford E, Taylor BA. A new capacity for plurisubharmonic functions. Acta Math. 1982;149:1–40.
  • Demailly J-P. Monge--Ampère operators, Lelong numbers and intersection theory. Complex analysis and geometry. New York (NY): Plenum; 1993. p. 115–193. (The University Series in Mathematics).
  • Cegrell U. Pluricomplex energy. Acta Math. 1998;180:187–217.
  • Cegrell U. The general definition of the complex Monge--Ampère operator. Ann Inst Fourier (Grenoble). 2004;54:159–179.
  • Błocki Z. Weak solutions to the complex Hessian equation. Ann Inst Fourier (Grenoble). 2005;55:1735–1756.
  • Dinew S, Kołodziej S. A priori estimates for the complex Hessian equations. Anal PDE. 2014;7:227–244.
  • Chinh LH. On Cegrell’s classes of m-subharmonic functions. 2012. arXiv 1301.6502v1.
  • Li SY. On the Dirichlet problems for symmetric function equations of the eigenvalues of the complex Hessian. Asian J Math. 2004;8:87–106.
  • Sadullaev AS, Abullaev BI. Potential theory in the class of m-subharmonic functions, Trudy Mathematicheskogo Instituta imeni V. A. Steklova. 2012;279:166–192.
  • Nguyen NC. Hölder continuous solutions to complex Hessian equations. Potential Anal. 2014;41:887–902.
  • Chinh LH. Viscosity solutions to complex Hessian equations. J Funct Anal. 2013;264:1355–1379.
  • Wang Y. A viscosity approach to the Dirichlet problem for complex Monge--Ampère Equations. Math Z. 2012;272:497–513.
  • Eyssidieux P, Guedj V, Zeriahi A. Viscosity solutions to degenerate complex Monge--Amp‘ere equations. Commun Pure Appl Math. 2011;64:1059–1094.
  • Kołodziej S. The Monge--Ampère equation on compact Kähler manifolds. Indiana U Math J. 2003;52:667–686.
  • Ahag P, Cegrell U, Czyz R, et al. Monge--Ampère measures on pluripolar sets. J Math Pures Appl. 2009;92:613–627.
  • Klimek M. Pluripotential theory. New York (NY): The Clarendon Press, Oxford University Press; 1991. Oxford Science Publications.
  • Kołodziej S. The range of the complex Monge-Ampère operator. II, Indiana Univ Math J. 1995;44:765–782.
  • Kołodziej S. The complex Monge--Ampère equation and pluripotential theory. Memoirs Am Math Soc. 2005;178:64p.
  • Hung VV. Local property of a class of m-subharmonic functions. Vietnam J Math. 2016;44(3):603–621.
  • Cegrell U, Kolodziej S, Zeriahi A. Subextension of plurisubharmonic functions with weak singularities. Math Z. 2005;250:7–22.
  • Cegrell U. On the discontinuity of the Monge--Ampère operator. Anal Complexe. 1094;1984:29–31.
  • Fornæss JE, Sibony N. Oka’s inequality for currents and applications. Math Ann. 1995;301:399–419.
  • H{\"o}rmander L. Notions of convexity. Basel: Birkhäuser; 1994.
  • Cegrell U. A general Dirichlet problem for the complex Monge--Ampère operator. Ann Pol Math. 2008;94:131–147.
  • Van Khue N, Hiep PH. A Comparision Principle for the complex Monge--Ampère operator in Cegrell’s classes and applications. Trans Am Math Soc. 2009;361:5539–5554.
  • Hai LM, Hong NX, Hung VV. Some characterizations of the class εm(Ω) and applications. Ann Polon Math. 2015;115:145–163.

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