Let $I$ be a bounded interval in the real line and $W$ a continuous non-negative function vanishing only at $a$, $b$. We obtain the asymptotic behaviour of the functionals $$ \F_\epsilon(u) := \epsilon \int_I \int_I { |u(x)-u(y)|^2 \over |x-y|^2 } dx dy + \lambda_\epsilon \int_I W(u) dx $$ when $\epsilon$ tends to $0$ and $\lambda_\epsilon$ satisfies $\log\lambda_\epsilon \sim k/\eps$ with $0 < k < +\infty$.
Un rèsultat de perturbations singuliéres avec la norme H^1/2
ALBERTI, GIOVANNI;
1994-01-01
Abstract
Let $I$ be a bounded interval in the real line and $W$ a continuous non-negative function vanishing only at $a$, $b$. We obtain the asymptotic behaviour of the functionals $$ \F_\epsilon(u) := \epsilon \int_I \int_I { |u(x)-u(y)|^2 \over |x-y|^2 } dx dy + \lambda_\epsilon \int_I W(u) dx $$ when $\epsilon$ tends to $0$ and $\lambda_\epsilon$ satisfies $\log\lambda_\epsilon \sim k/\eps$ with $0 < k < +\infty$.File in questo prodotto:
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