Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some counterexamples to the regularity of Monge-Ampère equations


Author: Xu Jia Wang
Journal: Proc. Amer. Math. Soc. 123 (1995), 841-845
MSC: Primary 35B65; Secondary 35J60
MathSciNet review: 1223269
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present examples to show that the solution u of the Monge-Ampère equation $ \det ({D^2}u) = f(x)$, with $ u = 0$ on the boundary, may not lie in $ {W^{2,p}}$ or in $ {C^{1,\alpha }}$ for noncontinuous and positive $ f(x)$ and for continuous and nonnegative $ f(x)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35B65, 35J60

Retrieve articles in all journals with MSC: 35B65, 35J60


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1223269-0
PII: S 0002-9939(1995)1223269-0
Keywords: Monge-Ampère equations, elliptic regularity, convexity
Article copyright: © Copyright 1995 American Mathematical Society