Interior regularity of solutions to a complex Monge-Ampère equation

Björn Ivarsson

doi:10.1007/BF02384537

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Home > Journals > Ark. Mat. > Volume 40 > Issue 2 > Article

October 2002 Interior regularity of solutions to a complex Monge-Ampère equation

Björn Ivarsson

Author Affiliations +

Björn Ivarsson¹
¹Department of Mathematics, Uppsala University

Ark. Mat. 40(2): 275-300 (October 2002). DOI: 10.1007/BF02384537

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Abstract

We give interior estimates for first derivatives of solutions to a type of complex Monge-Ampère equations in convex domains. We also show global estimates for first derivatives of solutions in arbitrary domains. These global estimates are then used to show interior regularity of solutions to the complex Monge-Ampère equations in hyperconvex domains having a bounded exhaustion function which is globally Lipschitz. Finally we give examples of domains which have such an exhaustion function and domains which do not.

Funding Statement

The author was partially supported by the Royal Swedish Academy of Sciences, Gustaf Sigurd Magnuson’s fund.

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Björn Ivarsson. "Interior regularity of solutions to a complex Monge-Ampère equation." Ark. Mat. 40 (2) 275 - 300, October 2002. https://doi.org/10.1007/BF02384537