arXiv:math/0305223 Abstract

arXiv:math/0305223 [math.AP]Abstract References Reviews Resources

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

Published 2003-05-15, updated 2004-02-11Version 2

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.

Comments: 23 pages

Categories: math.AP

Subjects: 35J60

Keywords: asymptotic estimates, qualitatives properties, semilinear elliptic problem, large exponent, level sets

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