Single-point condensation and least-energy solutions
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- by Xiaofeng Ren and Juncheng Wei PDF
- Proc. Amer. Math. Soc. 124 (1996), 111-120 Request permission
Abstract:
We prove a conjecture raised in our earlier paper which says that the least-energy solutions to a two-dimensional semilinear problem exhibit single-point condensation phenomena as the nonlinear exponent gets large. Our method is based on a sharp form of a well-known borderline case of the Sobolev embedding theory. With the help of this embedding, we can use the Moser iteration scheme to carefully estimate the upper bound of the solutions. We can also determine the location of the condensation points.References
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Additional Information
- Xiaofeng Ren
- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- Address at time of publication: Institute for Mathematics & Applications, University of Minnesota, Minneapolis, Minnesota 55455
- Email: ren@ima.umn.edu
- Juncheng Wei
- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- Address at time of publication: Department of Mathematics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong
- MR Author ID: 339847
- ORCID: 0000-0001-5262-477X
- Received by editor(s): July 2, 1994
- Communicated by: Jeffrey Rauch
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 111-120
- MSC (1991): Primary 35B40, 35A08, 35A15; Secondary 34A34
- DOI: https://doi.org/10.1090/S0002-9939-96-03156-5
- MathSciNet review: 1301045