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Boundary regularity of the solution to the complex Monge-Ampère equation on pseudoconvex domains of infinite type

Journal Article


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Abstract


  • All rights reserved. Let Ω be a C2-smooth, bounded, pseudoconvex domain in ℂn satisfying the "f -property". The f -property is a consequence of the geometric "type" of the boundary. All pseudoconvex domains of finite type satisfy the f-property as well as many classes of domains of infinite type. In this paper, we prove the existence, uniqueness, and "weak" Hölder-regularity up to the boundary of the solution to the Dirichlet problem for the complex Monge-Ampère equation (Formula Presented) The idea of our proof goes back to Bedford and Taylor [1]. However, the basic geometrical ingredient is based on a recent result by Khanh [12].

Publication Date


  • 2015

Citation


  • Ha, L. & Khanh, T. (2015). Boundary regularity of the solution to the complex Monge-Ampère equation on pseudoconvex domains of infinite type. Mathematical Research Letters, 22 (2), 467-484.

Scopus Eid


  • 2-s2.0-84928898606

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5548&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4527

Has Global Citation Frequency


Number Of Pages


  • 17

Start Page


  • 467

End Page


  • 484

Volume


  • 22

Issue


  • 2

Place Of Publication


  • United States

Abstract


  • All rights reserved. Let Ω be a C2-smooth, bounded, pseudoconvex domain in ℂn satisfying the "f -property". The f -property is a consequence of the geometric "type" of the boundary. All pseudoconvex domains of finite type satisfy the f-property as well as many classes of domains of infinite type. In this paper, we prove the existence, uniqueness, and "weak" Hölder-regularity up to the boundary of the solution to the Dirichlet problem for the complex Monge-Ampère equation (Formula Presented) The idea of our proof goes back to Bedford and Taylor [1]. However, the basic geometrical ingredient is based on a recent result by Khanh [12].

Publication Date


  • 2015

Citation


  • Ha, L. & Khanh, T. (2015). Boundary regularity of the solution to the complex Monge-Ampère equation on pseudoconvex domains of infinite type. Mathematical Research Letters, 22 (2), 467-484.

Scopus Eid


  • 2-s2.0-84928898606

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5548&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4527

Has Global Citation Frequency


Number Of Pages


  • 17

Start Page


  • 467

End Page


  • 484

Volume


  • 22

Issue


  • 2

Place Of Publication


  • United States