caa a22 4500 386382980 CHVBK 20180307112049.0 cr unu---uuuuu 161130s1989 xx s 000 0 eng 10.1017/S0308210500025026 doi S0308210500025026 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500025026 Local minimisers and singular perturbations [Elektronische Daten] We construct local minimisers to certain variational problems. The method is quite general and relies on the theory of Γ-convergence. The approach is demonstrated through the model problem It is shown that in certain nonconvex domains Ω ⊂ ℝn and for ε small, there exist nonconstant local minimisers uε satisfying uε ≈ ± 1 except in a thin transition layer. The location of the layer is determined through the requirement that in the limit uε →u0, the hypersurface separating the states u0 = 1 and u0 = −1 locally minimises surface area. Generalisations are discussed with, for example, vector-valued u and "anisotropic” perturbations replacing |∇u|2. Copyright © Royal Society of Edinburgh 1989 Kohn Robert V. Courant Institute, 251 Mercer Street, New York, NY 10012, U.S.A. Sternberg Peter Department of Mathematics, Stanford University, Stanford, CA 94305, U.S.A. Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 111/1-2(1989), 69-84 0308-2105 111:1-2<69 1989 111 PRM https://doi.org/10.1017/S0308210500025026 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500025026 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kohn Robert V. Courant Institute, 251 Mercer Street, New York, NY 10012, U.S.A NATIONALLICENCE 700 1- Sternberg Peter Department of Mathematics, Stanford University, Stanford, CA 94305, U.S.A NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 111/1-2(1989), 69-84 0308-2105 111:1-2<69 1989 111 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge