François Murat

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Two devices are currently available for the treatment of prostate cancer with HIFU: Sonablate® and Ablatherm®. The outcomes achieved for primary-care patient are very promissing with mid- and long-term progression-free survival rates around 70%, negative postoperative prostate biopsies almost 85%, and an excellent morbidity profile. Moreover, HIFU has a(More)
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)