Tornado solutions for semilinear elliptic equations in : Applications

Authors:
Frances Hammock, Peter Luthy, Alexander M. Meadows and Phillip Whitman

Journal:
Proc. Amer. Math. Soc. **135** (2007), 1419-1430

MSC (2000):
Primary 35J60, 26B05

DOI:
https://doi.org/10.1090/S0002-9939-06-08618-7

Published electronically:
October 27, 2006

MathSciNet review:
2276651

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show partial regularity of bounded positive solutions of some semilinear elliptic equations in domains of . As a consequence, there exists a large variety of nonnegative singular solutions to these equations. These equations have previously been studied from the point of view of free boundary problems, where solutions additionally are stable for a variational problem, which we do not assume.

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Additional Information

**Frances Hammock**

Affiliation:
Department of Mathematics, UCLA, Los Angeles, California 90095-1555

Email:
hammockf@math.ucla.edu

**Peter Luthy**

Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14850

Email:
pmlut@math.cornell.edu

**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

**Phillip Whitman**

Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 08540

Email:
pwhitman@math.princeton.edu

DOI:
https://doi.org/10.1090/S0002-9939-06-08618-7

Keywords:
Semilinear elliptic equations,
regularity theory,
singular solutions,
free boundary problems

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 REU grant DMS-0139229 at Cornell University

The third author 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.