Variational principles with integrands defined through a minimum

DOI10.1016/j.na.2006.04.007zbMath1112.49016OpenAlexW2089389632MaRDI QIDQ876954

Pablo Pedregal

Publication date: 19 April 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.04.007

zbMATH Keywords

convex hullgradient Young measuresnon-convexityminimum of a family of integrands

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45)

Cites Work

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• The relaxation of a double-well energy
• Parametrized measures and variational principles
• Minimizing a functional depending on \(\nabla u\) and on \(u\)
• A sharp attainment result for nonconvex variational problems
• Fully explicit quasiconvexification of the mean-square deviation of the gradient of the state in optimal design
• Constrained quasiconvexification of the square of the gradient of the state in optimal design
• Direct methods in the calculus of variations

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