Quand deux sous-variétés sont forcées par leur géométrie à se rencontrer
Quasistatic frictional problems for elastic and viscoelastic materials
We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational...
Quasi-static rate-independent evolutions: characterization, existence, approximation and application to fracture mechanics
We characterize quasi-static rate-independent evolutions, by means of their graph parametrization, in terms of a couple of equations: the first gives stationarity while the second provides the energy balance. An abstract existence result is given for functionals ℱ of class C1 in reflexive separable Banach spaces. We provide a couple of constructive proofs of existence which share common features with the theory of minimizing movements for gradient flows. Moreover, considering a sequence of functionals...
Quaternionic geometry of a nilpotent variety.
Quaternionic maps and minimal surfaces
Let and be hyperkähler manifolds. We study stationary quaternionic maps between and . We first show that if there are no holomorphic 2-spheres in the target then any sequence of stationary quaternionic maps with bounded energy subconverges to a stationary quaternionic map strongly in . We then find that certain tangent maps of quaternionic maps give rise to an interesting minimal 2-sphere. At last we construct a stationary quaternionic map with a codimension-3 singular set by using the embedded...
Quelques notions simples en géométrie riemannienne et leurs applications aux feuilletages compacts.
Recent existence and regularity results for wave maps
Rectification : «Algèbres de Clifford symplectiques et revêtements spinoriels du groupe symplectique»
Refined Kato inequalities in riemannian geometry
We describe the recent joint work of the author with David M. J. Calderbank and Paul Gauduchon on refined Kato inequalities for sections of vector bundles living in the kernel of natural first-order elliptic operators.
Régularité de la solution d'un problème variationnel
Regularity and Finiteness of Solutions to the Free Boundary Problem for Minimal Surfaces.
Regularity and uniqueness of harmonic maps into and ellipsoid.
Regularity at the free boundary of two-dimensional stationary harmonic maps
Regularity for a non linear variational problem in dimension two.
Regularity for Signorini's Problem in linear eleasticity.
Regularity of a Minimal Surface at its Free Boundary.
Regularity of constraints and reduction in the Minkowski space Yang-Mills-Dirac theory
Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type
We prove the hypoellipticity for systems of Hörmander type with constant coefficients in Carnot groups of step 2. This result is used to implement blow-up methods and prove partial regularity for local minimizers of non-convex functionals, and for solutions of non-linear systems which appear in the study of non-isotropic metric structures with scalings. We also establish estimates of the Hausdorff dimension of the singular set.
Regularity of minimizing harmonic maps into S4, S5 and symmetric spaces.
Regularity of minimizing harmonic maps into the sphere.