Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Tornado solutions for semilinear elliptic equations in $ \mathbb{R}^2$: regularity

Author: Alexander M. Meadows
Journal: Proc. Amer. Math. Soc. 135 (2007), 1411-1417
MSC (2000): Primary 35J60, 26B05
Published electronically: October 27, 2006
MathSciNet review: 2276650
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give conditions under which bounded solutions to semilinear elliptic equations $ \Delta u = f(u)$ on domains of $ \mathbb{R}^2$ are continuous despite a possible infinite singularity of $ f(u)$. The conditions do not require a minimization or variational stability property for the solutions. The results are used in a second paper to show regularity for a familiar class of equations.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35J60, 26B05

Retrieve articles in all journals with MSC (2000): 35J60, 26B05

Additional Information

Alexander M. Meadows
Affiliation: Department of Mathematics and Computer Science, St. Mary’s College of Maryland, St. Mary’s City, Maryland 20686

Keywords: Semilinear elliptic equations, regularity theory, singular solutions
Received by editor(s): September 11, 2005
Received by editor(s) in revised form: December 5, 2005
Published electronically: October 27, 2006
Additional Notes: This work was partially supported by NSF grants DMS-9983660 and DMS-0306495 at Cornell University
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society