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Hölder regularity of the solution to the complex Monge-Ampère equation with L p density

Journal Article


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Abstract


  • On a smooth domain ⊂⊂ Cn,we consider the Dirichlet problem for the complex

    Monge-Ampère equation ((ddcu)n = f dV, u|b ≡ φ). We state the Hölder regularity of

    the solution u when the boundary value φ is Hölder continuous and the density f is only

    L p, p > 1. Note that in former literature (Guedj-Kolodziej-Zeriahi) the weakness of the

    assumption f ∈ L p was balanced by taking φ ∈ C1,1 (in addition to assuming strongly

    pseudoconvex).

Authors


  •   Baracco, Luca (external author)
  •   Khanh, Tran Vu
  •   Pinton, Stefano (external author)
  •   Zampieri, Giuseppe (external author)

Publication Date


  • 2016

Citation


  • Baracco, L., Khanh, T., Pinton, S. & Zampieri, G. (2016). Hölder regularity of the solution to the complex Monge-Ampère equation with L p density. Calculus of Variations and Partial Differential Equations, 55 (4), 74-1-74-8.

Scopus Eid


  • 2-s2.0-84975804526

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=6994&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5965

Has Global Citation Frequency


Start Page


  • 74-1

End Page


  • 74-8

Volume


  • 55

Issue


  • 4

Place Of Publication


  • Berlin, Germany

Abstract


  • On a smooth domain ⊂⊂ Cn,we consider the Dirichlet problem for the complex

    Monge-Ampère equation ((ddcu)n = f dV, u|b ≡ φ). We state the Hölder regularity of

    the solution u when the boundary value φ is Hölder continuous and the density f is only

    L p, p > 1. Note that in former literature (Guedj-Kolodziej-Zeriahi) the weakness of the

    assumption f ∈ L p was balanced by taking φ ∈ C1,1 (in addition to assuming strongly

    pseudoconvex).

Authors


  •   Baracco, Luca (external author)
  •   Khanh, Tran Vu
  •   Pinton, Stefano (external author)
  •   Zampieri, Giuseppe (external author)

Publication Date


  • 2016

Citation


  • Baracco, L., Khanh, T., Pinton, S. & Zampieri, G. (2016). Hölder regularity of the solution to the complex Monge-Ampère equation with L p density. Calculus of Variations and Partial Differential Equations, 55 (4), 74-1-74-8.

Scopus Eid


  • 2-s2.0-84975804526

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=6994&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5965

Has Global Citation Frequency


Start Page


  • 74-1

End Page


  • 74-8

Volume


  • 55

Issue


  • 4

Place Of Publication


  • Berlin, Germany