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)

 

$ n$-Laplacian in $ \mathcal{H}\sp 1\sb \mathrm{loc}$ does not lead to regularity


Author: Nikan B. Firoozye
Journal: Proc. Amer. Math. Soc. 123 (1995), 3357-3360
MSC: Primary 35J05; Secondary 42B30
MathSciNet review: 1277110
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is well known that in two space dimensions, if a solution to Poisson's equation has right-hand side in $ \mathcal{H}_{{\text{loc}}}^1$, then this solution is actually continuous. The corresponding result for n-Laplacians is shown to be false for $ n \geq 3$; we construct two examples with right-hand sides in $ \mathcal{H}_{{\text{loc}}}^1({\Re ^n})$ such that the corresponding solutions to the n-Laplacian are unbounded in the first case, and bounded but discontinuous in the second.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35J05, 42B30

Retrieve articles in all journals with MSC: 35J05, 42B30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1277110-0
PII: S 0002-9939(1995)1277110-0
Article copyright: © Copyright 1995 American Mathematical Society