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), 14191430
MSC (2000):
Primary 35J60, 26B05
Published electronically:
October 27, 2006
MathSciNet review:
2276651
Fulltext PDF Free Access
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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 900951555
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:
http://dx.doi.org/10.1090/S0002993906086187
PII:
S 00029939(06)086187
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 DMS0139229 at Cornell University
The third author was partially supported by NSF grants DMS9983660 and DMS0306495 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.
