We consider variational problems defined on domains 'weakly' connected through a separation hyperplane ('sieve plane') by an ε-periodically distributed 'contact zone'. We study the asymptotic behaviour as e tends to 0 of integral functional in such domains in the nonlinear and vector-valued case, showing that the asymptotic memory of the sieve is described by a nonlinear 'capacitary-type' formula. In particular we treat the case when the integral energies on both sides of the sieve plane satisfy different growth conditions. We also study the case of thin films, with flat profile and thickness ε, connected by the same sieve plane.
The nonlinear sieve problem and applications to thin films / Ansini, Nadia. - In: ASYMPTOTIC ANALYSIS. - ISSN 0921-7134. - 39:2(2004), pp. 113-145.
The nonlinear sieve problem and applications to thin films
ANSINI, NADIA
2004
Abstract
We consider variational problems defined on domains 'weakly' connected through a separation hyperplane ('sieve plane') by an ε-periodically distributed 'contact zone'. We study the asymptotic behaviour as e tends to 0 of integral functional in such domains in the nonlinear and vector-valued case, showing that the asymptotic memory of the sieve is described by a nonlinear 'capacitary-type' formula. In particular we treat the case when the integral energies on both sides of the sieve plane satisfy different growth conditions. We also study the case of thin films, with flat profile and thickness ε, connected by the same sieve plane.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.