In this paper, we consider a nonlinear traction problem for the Lam'e equations in a periodically perforated domain obtained by making in $mathbbR^n$ a periodic set of holes, each of them of size proportional to $epsilon$. Under suitable assumptions, we know that there exists a family of solutions $\u(epsilon,cdot)_epsilonin]0,epsilon_1[$ with a prescribed limiting behavior when $epsilon$ approaches $0$. Then we investigate the energy integral of $u(epsilon,cdot)$ as $epsilon$ tends to $0$, and we prove that such integral can be continued real analytically for negative values of $epsilon$.

Energy integral of a nonlinear traction problem in a singularly perturbed periodically perforated domain

Musolino P.
2014

Abstract

In this paper, we consider a nonlinear traction problem for the Lam'e equations in a periodically perforated domain obtained by making in $mathbbR^n$ a periodic set of holes, each of them of size proportional to $epsilon$. Under suitable assumptions, we know that there exists a family of solutions $\u(epsilon,cdot)_epsilonin]0,epsilon_1[$ with a prescribed limiting behavior when $epsilon$ approaches $0$. Then we investigate the energy integral of $u(epsilon,cdot)$ as $epsilon$ tends to $0$, and we prove that such integral can be continued real analytically for negative values of $epsilon$.
Complex Analysis and Potential Theory with applications, Proceedings of the 9th ISAAC Congress
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/3723641
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