Proceedings of the American Mathematical Society

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

Author(s): Alexander M. Meadows
Journal: Proc. Amer. Math. Soc. 135 (2007), 1411-1417.
MSC (2000): Primary 35J60, 26B05
Posted: October 27, 2006
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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

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

Alexander M. Meadows
Affiliation: Department of Mathematics and Computer Science, St. Mary's College of Maryland, St. Mary's City, Maryland 20686
Email: ammeadows@smcm.edu

DOI: 10.1090/S0002-9939-06-08617-5
PII: S 0002-9939(06)08617-5
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
Posted: 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
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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