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Boundary C2,α estimates for Monge–Ampère type equations

Journal Article


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Abstract


  • In this paper, we obtain global second derivative estimates for solutions of the Dirichlet problem of certain Monge–Ampère type equations under some structural conditions, while the inhomogeneous term is only assumed to be Hölder continuous and bounded away from zero and infinity. These estimates correspond to those for the standard Monge–Ampère equation obtained by Trudinger and Wang (2008) and by Savin (2013), and have natural applications in optimal transportation and prescribed Jacobian equations.

Authors


  •   Huang, Yong (external author)
  •   Jiang, Feida (external author)
  •   Liu, Jiakun

Publication Date


  • 2015

Citation


  • Huang, Y., Jiang, F. & Liu, J. (2015). Boundary C2,α estimates for Monge–Ampère type equations. Advances in Mathematics, 281 706-733.

Scopus Eid


  • 2-s2.0-84930959232

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5266&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4245

Has Global Citation Frequency


Number Of Pages


  • 27

Start Page


  • 706

End Page


  • 733

Volume


  • 281

Place Of Publication


  • United Kingdom

Abstract


  • In this paper, we obtain global second derivative estimates for solutions of the Dirichlet problem of certain Monge–Ampère type equations under some structural conditions, while the inhomogeneous term is only assumed to be Hölder continuous and bounded away from zero and infinity. These estimates correspond to those for the standard Monge–Ampère equation obtained by Trudinger and Wang (2008) and by Savin (2013), and have natural applications in optimal transportation and prescribed Jacobian equations.

Authors


  •   Huang, Yong (external author)
  •   Jiang, Feida (external author)
  •   Liu, Jiakun

Publication Date


  • 2015

Citation


  • Huang, Y., Jiang, F. & Liu, J. (2015). Boundary C2,α estimates for Monge–Ampère type equations. Advances in Mathematics, 281 706-733.

Scopus Eid


  • 2-s2.0-84930959232

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5266&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4245

Has Global Citation Frequency


Number Of Pages


  • 27

Start Page


  • 706

End Page


  • 733

Volume


  • 281

Place Of Publication


  • United Kingdom