A variational model for linearly elastic micropolar plate-like bodies

We consider a micropolar, linearly elastic plate-like body, clamped on its boundary and subject to a system of distance loads. We characterize, by means of Γ-convergence, the limit behavior of the solutions of the equilibrium problem when the thickness of the body vanishes. We show that, for the special case of isotropic mechanical response, the equilibrium problem described by our Γ-limit coincides with a boundary-value problem obtained in a recent deduction of a theory for shearable plates from micropolar elasticity

Micropolar linearly elastic rods

We use Γ-convergence to recover the behaviour of solutions of the equilibrium problem for a linearly elastic micropolar ro

Micropolar linearly elastic rods

We use Γ-convergence to recover the behaviour of solutions of the equilibrium problem for a linearly elastic micropolar ro

Normalized solutions to mass supercritical Schroedinger equations with negative potential

We study the existence of positive solutions with prescribed L-2-norm for the mass supercritical Schrodinger equation -delta u+lambda u - V(x)u = |u|(p-2)u u is an element of H-1(R-N), lambda is an element of R, where V >= 0, N >= 1 and p is an element of(2+4/N, 2*), 2*: = 2N/N-2 if N >= 3 and 2* : = +infinity if N = 1,2. We treat two cases. Firstly, under an explicit smallness assumption on V and no condition on the mass, we prove the existence of a mountain pass solution at positive energy level, and we exclude the existence of solutions with negative energy. Secondly, requiring that the mass is smaller than some explicit bound, depending on V, and that V is not too small in a suitable sense, we find two solutions: a local minimizer with negative energy, and a mountain pass solution with positive energy. Moreover, a nonexistence result is proved

Asymptotic behaviour of a thin insulation problem

We consider a problem of thermal insulation and we study, by means of Gamma-convergence, the best way to put the insulator when its mass tends to zero

A variational model for linearly elastic micropolar plate-like bodies

We consider a micropolar, linearly elastic plate-like body, clamped on its boundary and subject to a system of distance loads. We characterize, by means of Γ-convergence, the limit behavior of the solutions of the equilibrium problem when the thickness of the body vanishes. We show that, for the special case of isotropic mechanical response, the equilibrium problem described by our Γ-limit coincides with a boundary-value problem obtained in a recent deduction of a theory for shearable plates from micropolar elasticity

First variation of anisotropic energies and crystalline mean curvature for partitions

We rigorously derive the notion of crystalline mean curvature of an anisotropic partition with no restriction on the space dimension. Our results cover the case of crystalline networks in two dimensions, polyhedral partitions in three dimensions, and generic anisotropic partitions for smooth anisotropies. The natural equilibrium conditions on the singular set of the partition are derived. We discuss several examples in two dimensions (also for two adjacent triple junctions) and one example in three dimensions when the Wulff shape is the unit cube. In the examples we also analyze the stability of the partitions

First variation of anisotropic energies and crystalline mean curvature for partitions

We rigorously derive the notion of crystalline mean curvature of an anisotropic partition with no restriction on the space dimension. Our results cover the case of crystalline networks in two dimensions, polyhedral partitions in three dimensions, and generic anisotropic partitions for smooth anisotropies. The natural equilibrium conditions on the singular set of the partition are derived. We discuss several examples in two dimensions (also for two adjacent triple junctions) and one example in three dimensions when the Wulff shape is the unit cube. In the examples we also analyze the stability of the partitions