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Single-point condensation and least-energy solutions
Author(s):
Xiaofeng
Ren;
Juncheng
Wei
Journal:
Proc. Amer. Math. Soc.
124
(1996),
111-120.
MSC (1991):
Primary 35B40, 35A08, 35A15;
Secondary 34A34
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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
DOI:
10.1090/S0002-9939-96-03156-5
PII:
S 0002-9939(96)03156-5
Received by editor(s):
July 2, 1994
Communicated by:
Jeffrey Rauch
Copyright of article:
Copyright
1996,
American Mathematical Society
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