Local Minimizers Induced by Spatial Inhomogeneity with Inner Transition Layer

Abstract

otherwise, where k 1 and k 2 are positive functions in C 2 (0 , R), 0: an open bounded subset of R 2 with a Lipschitz-continuous boundary. article no. DE963206 203 0022-0396Â97 25.00

Singular perturbation and bifurcation of diffuse transition layers in inhomogeneous media, part I

“…This is one example using the machinery commonly known as SLEP (singular limit eigenvalue problem [13]). There are quite a few higher dimensional analogue of the above results, see for example, do Nascimento [19,20], and Li-Nakashima [17] In all of the above works, various types of non-degeneracy conditions on the limiting interfacial problem are assumed. It is interesting and important to investigate the behavior and existence of layers when degeneracy occurs.…”