The authors study the asymptotic behavior as ε→0+ of the multidimensional minimization problem min∫Ω[f(x/ε,Du(x))+g(x)u(x)]dx under the Dirichlet condition u=0 on ∂Ω and under a pointwise constraint |Du|≤φ on the gradient. The integrand f is assumed to be 1-periodic in the space variables and to satisfy the standard hypotheses of strict convexity, coerciveness and boundedness; the constraint φ is also assumed to be 1-periodic. The results are similar to earlier ones by the same authors, but here the constraint φ is allowed to be +∞ (i.e. no constraint) on a subcube [12−θ,12+θ]n of the periodicity cube [0,1]n.
Homogenizatíon with unbounded constraints on the gradient
SALERNO, Saverio
1985-01-01
Abstract
The authors study the asymptotic behavior as ε→0+ of the multidimensional minimization problem min∫Ω[f(x/ε,Du(x))+g(x)u(x)]dx under the Dirichlet condition u=0 on ∂Ω and under a pointwise constraint |Du|≤φ on the gradient. The integrand f is assumed to be 1-periodic in the space variables and to satisfy the standard hypotheses of strict convexity, coerciveness and boundedness; the constraint φ is also assumed to be 1-periodic. The results are similar to earlier ones by the same authors, but here the constraint φ is allowed to be +∞ (i.e. no constraint) on a subcube [12−θ,12+θ]n of the periodicity cube [0,1]n.File in questo prodotto:
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