Asymptotic Estimates and Qualitatives Properties of an Elliptic Problem in Dimension Two

Details Asymptotic Estimates and Qualitatives Properties of an Elliptic Problem in Dimension Two Asymptotic Estimates and Qualitatives Properties of an Elliptic Problem in Dimension Two

2003-05-15

arxiv.org/abs/math/0305223v2

Mathematics

Analysis of PDEs

23 pages

Scientific paper

In this paper we study a semilinear elliptic problem on a bounded domain in $\R^2$ with large exponent in the nonlinear term. We consider positive solutions obtained by minimizing suitable functionals. We prove some asymtotic estimates which enable us to associate a "limit problem" to the initial one. Usong these estimates we prove some quantitative properties of the solution, namely characterization of level sets and nondegeneracy.

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