We study the asymptotic behavior as epsilon --> 0 of highly oscillating periodic nonlinear functionals of the form F-epsilon(u) = integral(Omega)f(x/epsilon, Du(x)) dx, defined on a Sobolev space W-1,W-p(Omega;R(m)). We characterise their variational limit under the hypotheses that there exists a c such that the region where f(x,xi) less than or equal to c(1 + xi(p)) does not hold for all matrices xi is composed of well-separated sets, and the condition f(x,xi) greater than or equal to xi(p) for all matrices xi is verified on a connected open set with Lipschitz boundary.
HOMOGENIZATION OF PERIODIC NONLINEAR MEDIA WITH STIFF AND SOFT INCLUSIONS / Andrea, Braides; Garroni, Adriana. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 5:04(1995), pp. 543-564. [10.1142/s0218202595000322]
HOMOGENIZATION OF PERIODIC NONLINEAR MEDIA WITH STIFF AND SOFT INCLUSIONS
GARRONI, Adriana
1995
Abstract
We study the asymptotic behavior as epsilon --> 0 of highly oscillating periodic nonlinear functionals of the form F-epsilon(u) = integral(Omega)f(x/epsilon, Du(x)) dx, defined on a Sobolev space W-1,W-p(Omega;R(m)). We characterise their variational limit under the hypotheses that there exists a c such that the region where f(x,xi) less than or equal to c(1 + xi(p)) does not hold for all matrices xi is composed of well-separated sets, and the condition f(x,xi) greater than or equal to xi(p) for all matrices xi is verified on a connected open set with Lipschitz boundary.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
