Tornado solutions for semilinear elliptic equations in : 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 | References | Similar Articles | Additional Information

Abstract: We give conditions under which bounded solutions to semilinear elliptic equations on domains of 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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Additional Information

**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:
http://dx.doi.org/10.1090/S0002-9939-06-08617-5

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

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.