Premium
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom