Let $I$ be an open bounded interval of $\mathbb{R}$ and $W$ a non-negative continuous function vanishing only at $\alpha, \beta \in \mathbb{R}$. We investigate the asymptotic behaviour in terms of $\Gamma$-convergence of the following functional $$\dys G_{\epsilon}(u):=\epsilon^{p-2}\!\!\int\!\!\!\int_{I\times I}\!\left|\frac{u(x)-u(y)}{x-y}\right|^{p}\!\!dxdy+\frac{1}{\epsilon}\!\!\int_{I}\!W(u)\,dx \ \ (p>2),$$ as $\epsilon\to0$.

A singular perturbation result with a fractional norm / Adriana, Garroni; Palatucci, Giampiero. - STAMPA. - 68:(2006), pp. 111-126.

### A singular perturbation result with a fractional norm

#### Abstract

Let $I$ be an open bounded interval of $\mathbb{R}$ and $W$ a non-negative continuous function vanishing only at $\alpha, \beta \in \mathbb{R}$. We investigate the asymptotic behaviour in terms of $\Gamma$-convergence of the following functional $$\dys G_{\epsilon}(u):=\epsilon^{p-2}\!\!\int\!\!\!\int_{I\times I}\!\left|\frac{u(x)-u(y)}{x-y}\right|^{p}\!\!dxdy+\frac{1}{\epsilon}\!\!\int_{I}\!W(u)\,dx \ \ (p>2),$$ as $\epsilon\to0$.
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A singular perturbation result with a fractional norm / Adriana, Garroni; Palatucci, Giampiero. - STAMPA. - 68:(2006), pp. 111-126.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2742104