Alberti, Giovanni; Bouchitté, Guy; Seppecher, Pierre A singular perturbation result involving the \(H^{1/2}\) norm. (Un résultat de perturbations singulières avec la norme \(H^{1/2}\).) (French. Abridged English version) Zbl 0845.49008 C. R. Acad. Sci., Paris, Sér. I 319, No. 4, 333-338 (1994). Summary: Let \(I\) be a bounded interval of \(\mathbb{R}\) and \(W\) a continuous non-negative function vanishing only at \(\alpha, \beta\in \mathbb{R}\). We obtain the asymptotic behaviour of the functionals \[ F^\varepsilon(u):= \varepsilon \int \int_{I\times I} \Biggl|{u(x)- u(y)\over x- y}\Biggr|^2 dx dy+ \lambda_\varepsilon \int_I W(u) dx \] when \(\varepsilon\to 0\), \(\lambda_\varepsilon\to +\infty\) and \(\varepsilon\log \lambda_\varepsilon\to k\) \((0< k< + \infty)\). Cited in 3 ReviewsCited in 21 Documents MSC: 49J45 Methods involving semicontinuity and convergence; relaxation Keywords:integral functional; lower semicontinuity; \(\Gamma\)-convergence; gamma-convergence; singular perturbation; \(H^{1/2}\)-norm PDFBibTeX XMLCite \textit{G. Alberti} et al., C. R. Acad. Sci., Paris, Sér. I 319, No. 4, 333--338 (1994; Zbl 0845.49008)