On critical points of functionals with polyconvex integrands
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Submission date: 08. Jan. 2001
published in: Journal of convex analysis, 9 (2002) 1, p. 55-72
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We study implications of a function being a critical point of an integral functional with a polyconvex integrand. When the integrand depends on the spatial variable as well, we construct a counterexample establishing that the positivity of the second variation is not sufficient for a smooth critical point to be a strong local minimizer.