Tornado solutions for semilinear elliptic equations in $\mathbb {R}^2$: Applications
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- by Frances Hammock, Peter Luthy, Alexander M. Meadows and Phillip Whitman PDF
- Proc. Amer. Math. Soc. 135 (2007), 1419-1430 Request permission
Abstract:
We show partial regularity of bounded positive solutions of some semilinear elliptic equations $\Delta u = f(u)$ in domains of $\mathbb {R}^2$. 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.References
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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
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2276651