Tornado solutions for semilinear elliptic equations in $\mathbb {R}^2$: regularity
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- by Alexander M. Meadows PDF
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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 $f(u)$. 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.References
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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
- 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
- © 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), 1411-1417
- MSC (2000): Primary 35J60, 26B05
- DOI: https://doi.org/10.1090/S0002-9939-06-08617-5
- MathSciNet review: 2276650