Abstract :
The main aim of this paper is to construct and provide the structure of local minimizers of the variational problem infv L1(Ω) F (v), where : small parameter and[formula]having only the functionsk1>0 andk2>0 as parameters. Given any closed simple smooth curveγmcontained in a level set ofa(X)=k1(X) k2(X),X Ω, we give necessary conditions relating the slope and concavity ofa(X),X γm, along the normaln[γm(X)], with the curvatureκ(X) ofγmso that the above problem possesses a nonconstant minimizerv (X) whose nodal curveγ mconverges uniformly toγm, as →0. Moreoverv →1, as →0, uniformly on compact sets contained in one of the two connected components ofΩ\γmandv →−1, as →0, uniformly on compact sets contained in the other one.
