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The Bieberbach-Rademacher problem for the Monge-Ampère operator

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Abstract

Assume that Ω is a bounded, strictly convex, smooth domain in ℝN withN≥2. We consider the problem det ((∂ iju(x)))=f(x,u(x)),u(x)→∞ asx→∂Ω, where (∂ iju(x)) denotes the Hessian ofu(x) andf meets some natural regularity and growth conditions. We prove that there exists a unique smooth, strictly convex solution of this problem. The boundary-blow-up rate ofu(x) is characterized in terms of the distance ofx from ∂Ω.

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Authors and Affiliations

  1. Department of Mathematics, Uppsala University, P.O. Box 480, S-75106, Uppsala, Sweden

    Jerk Matero

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  1. Jerk Matero
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Partially supported by the Royal Swedish Academy of Sciences, Gustaf Sigurd Magnuson's fund.

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Matero, J. The Bieberbach-Rademacher problem for the Monge-Ampère operator. Manuscripta Math 91, 379–391 (1996). https://doi.org/10.1007/BF02567962

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