We study integral functionals constrained to divergence-free vector fields in
on a thin domain, under standard -growth and coercivity assumptions, 1 ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in
is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting...
We study integral functionals constrained to divergence-free vector fields in
on a thin domain, under standard -growth and coercivity assumptions, 1 ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in
is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting...
We derive sharp necessary conditions for weak sequential lower semicontinuity of integral functionals on Sobolev spaces, with an integrand which only depends on the gradient of a scalar field over a domain in . An emphasis is put on domains with infinite measure, and the integrand is allowed to assume the value .
We consider a class of second-gradient elasticity models for which the internal potential energy is taken as the sum of a convex function of the second gradient of the deformation and a general function of the gradient. However, in consonance with classical nonlinear elasticity, the latter is assumed to grow unboundedly as the determinant of the gradient approaches zero. While the existence of a minimizer is routine, the existence of weak solutions is not, and we focus our efforts on that question...
We consider a class of second-gradient elasticity models for which the internal potential energy is taken as the sum of a convex function of the second gradient of the deformation and a general function of the gradient. However, in consonance with classical nonlinear elasticity, the latter is assumed to grow unboundedly as the determinant of the gradient approaches zero. While the existence of a minimizer is routine, the existence of weak solutions is not, and we focus our efforts on that question...
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