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Bellido, José Carlos

Explicit computation of the relaxed density coming from a three-dimensional optimal design problem. (English) Zbl 1016.49015

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 52, No. 7, 1709-1726 (2003).
Summary: We analyze the relaxation of a typical three-dimensional optimal design problem in conductivity, consisting of minimizing the square of the \(L^2\)-norm of the underlying electric potential under a volume constraint, via a variational reformulation of the problem. Our main achievement is the explicit characterization of the “constrained quasiconvexification” of the cost density.

Cited in 6 Documents

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
49Q20 Variational problems in a geometric measure-theoretic setting
78A25 Electromagnetic theory (general)

Keywords:

optimal design; dependence on the gradient of the state; divergence-free; relaxation; conductivity; constrained quasiconvexification; Young measure
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Full Text: DOI

References:

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