Boundary Behavior of Large Solutions to the Monge-Ampère Equation in a Borderline Case
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This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge-Ampère equation detD2u(x) = b(x)f (u(x)), u > 0, x ∈ Ω, where Ω is a strictly convex and bounded smooth domain in ℝN with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and b ∈ C∞ (Ω) is positive in Ω, but may be appropriate singular on the boundary.
KeywordsThe Monge-Ampère equations strictly convex large solutions a borderline case boundary behavior
MR(2010) Subject Classification35J60 35B40 35J67 35B65
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- Bingham, N. H., Goldie, C. M., Teugels, J. L.: Regular Variation, Encyclopedia of Mathematics and its Applications 27, Cambridge University Press, Cambridge, 1987Google Scholar
- Cheng, S. Y., Yau, S. T.: The real Monge-Ampère equation and affine flat structures, in: Chern, S.S., Wu, W. (eds.), Proceedings of 1980 Beijing Symposium on Differential Geometry and Differential Equations, vol. 1, pp. 339–370, Beijing. Science Press, New York, 1982Google Scholar
- Seneta, R.: Regular Varying Functions, Lecture Notes in Math., vol. 508, Springer-Verlag, 1976Google Scholar
- Zhang, Z.: A unified boundary behavior of large solutions to Hessian equations. Chin. Ann. Math. B, in pressGoogle Scholar