Abstract
AbstractWe study the regularity and behavior at the origin of solutions to the two‐dimensional degenerate Monge‐Ampère equation det D2u = |x|α with α > −2. We show that when α > 0, solutions admit only two possible behaviors near the origin, radial and nonradial, which in turn implies C2, δ‐regularity. We also show that the radial behavior is unstable. For α < 0 we prove that solutions admit only the radial behavior near the origin. © 2008 Wiley Periodicals, Inc.
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