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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
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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.

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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.