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On Monge‐Ampère equations with homogenous right‐hand sides
Author(s) -
Daskalopoulos Panagiota,
Savin Ovidiu
Publication year - 2009
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20263
Subject(s) - degenerate energy levels , mathematics , ampere , mathematical analysis , pure mathematics , mathematical physics , physics , current (fluid) , thermodynamics , quantum mechanics
We study the regularity and behavior at the origin of solutions to the two‐dimensional degenerate Monge‐Ampère equation det D 2 u = | 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 C 2, 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.