François Murat

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This paper is devoted to the asymptotic analysis of the problem of linear elasticity for an anisotropic and inhomogeneous body occupying, in its reference configuration, a cylindrical domain with a rectangular cross section with sides proportional to ε and ε 2 and clamped on one of its bases. The sequence of solutions u ε of the equilibrium problem is shown(More)
We consider the linearized elasticity system in a multidomain of R 3. This multidomain is the union of a horizontal plate with fixed cross section and small thickness ε, and of a vertical beam with fixed height and small cross section of radius r ε. The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and r ε tend to(More)
We prove the existence of distributional solutions to an elliptic problem with a lower order term which depends on the solution u in a singular way and on its gradient Du with quadratic growth. The prototype of the problem under consideration is 8 < : −∆u + λu = ± |Du| 2 |u| k + f in Ω, u = 0 on ∂Ω, where λ > 0, k > 0, f (x) ∈ L ∞ (Ω), f (x) ≥ 0 (and so u ≥(More)
(see [3] and [4]), we consider the semilinear elliptic equation with homogeneous Dirichlet boundary condition −divA(x)Du = F (x, u) in Ω, u = 0 on ∂Ω, u ≥ 0 in Ω, where the nonlinearity F (x, u) is singular at u = 0, and more precisely where F is a 1 , Lipschitz-continuous, nondecreasing function such that Γ(0) = 0 and Γ(s) > 0 for every s > 0. A model for(More)