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 differential forms minimizing degenerate elliptic functionals.
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.
Regularity of Minimzing Harmonic Mappings into ellipsoids and similar other manifolds.
Regularity of p-harmonic maps from the p-dimensional ball into a sphere.
Regularity of p-harmonic maps into certain manifolds with positive sectional curvature.
Regularity of sets with constant intrinsic normal in a class of Carnot groups
In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano in step...
Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics
We discuss the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of the time-dependent Schrödinger equation in quantum molecular dynamics. This method approximates the high-dimensional nuclear wave function by a linear combination of products of functions depending only on a single degree of freedom. The equations of motion, obtained via the Dirac-Frenkel time-dependent variational principle, consist of a coupled system of low-dimensional nonlinear partial differential...
Regularity of weak H-surfaces.
Regularity of weakly harmonic maps from a surface into a manifold with symmetries.
Regularity properties of optimal transportation problems arising in hedonic pricing models
We study a form of optimal transportation surplus functions which arise in hedonic pricing models. We derive a formula for the Ma–Trudinger–Wang curvature of these functions, yielding necessary and sufficient conditions for them to satisfy (A3w). We use this to give explicit new examples of surplus functions satisfying (A3w), of the form b(x,y) = H(x + y) where H is a convex function on ℝn. We also show that the distribution of equilibrium contracts in this hedonic pricing model is absolutely continuous...
Regularity properties of the generalized hamiltonian flow
Regularity Theorems in Riemannian Geometry. II. Harmonic Curvature and the Weyl Tensor.
Relating quantum and braided Lie algebras
We outline our recent results on bicovariant differential calculi on co-quasitriangular Hopf algebras, in particular that if is a quantum tangent space (quantum Lie algebra) for a CQT Hopf algebra A, then the space is a braided Lie algebra in the category of A-comodules. An important consequence of this is that the universal enveloping algebra is a bialgebra in the category of A-comodules.
Relation de Poisson pour l'équation des ondes dans un ouvert non borné. Application au scattering