Local minimizers induced by spatial inhomogeneity with inner transition layer

[摘要] The main aim of this paper is to construct and provide the structure of local minimizers of the variational problem inf(epsilon is an element of L'(Omega))F-epsilon(v), where epsilon: small parameter and [graphics] having only the functions k(1) > 0 and k(2) > 0 as parameters. Given any closed simple smooth curve gamma(m) contained in a level set of a(X)=k(1)(X)k(2)(X), X is an element of Omega(1) we give necessary conditions relating the slope and concavity of a(X), X is an element of gamma(m), along the normal (n) over cap[gamma(m)(X)], with the curvature kappa(X) of gamma(m) so that the above problem possesses a nonconstant minimizer v(epsilon)(X) whose nodal curve gamma(m)(epsilon) converges uniformly to gamma(m), as epsilon --> 0. Moreover v --> 1, as epsilon --> 0, uniformly on compact sets contained in one of the two connected components of Omega\gamma(m) and v(epsilon)--> -1, as epsilon --> 0, uniformly on compact sets contained in the other one. (C) 1997 Academic Press

[发布日期] 1997-01-20