Smoothness of Itô maps and diffusion processes on path spaces (I)
Sobolev-Kantorovich Inequalities
In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds by means...
Solitons on pseudo-Riemannian manifolds: Stability and motion.
Solution explicite de l'équation des ondes dans un espace symétrique de type non compact de rang 1
Solutions globales de systèmes non linéaires sur des variétés hyperboliques
Solutions of elliptic equations on manifolds with roughly Euclidean ends.
Solutions of the constraint equations in general relativity satisfying "hyperboloidal boundary conditions" [Book]
Solvability of the Navier-Stokes equations on manifolds with boundary.
Solvable nonlinear evolution PDEs in multidimensional space.
Solving -Laplacian equations on complete manifolds.
Some applications of large sieve in Riemann surfaces
Some curvature identities for commutative spaces
Some decay properties for the damped wave equation on the torus
This article is a proceedings version of the ongoing work [1], and has been the object of a talk of the second author during the Journées “Équations aux Dérivées Partielles” (Biarritz, 2012).We address the decay rates of the energy of the damped wave equation when the damping coefficient does not satisfy the Geometric Control Condition (GCC). First, we give a link with the controllability of the associated Schrödinger equation. We prove that the observability of the Schrödinger group implies that...
Some differential operators connected with quasiconformal deformations on manifold
Some existence results for the scalar curvature problem via Morse theory
We prove existence of positive solutions for the equation on , arising in the prescribed scalar curvature problem. is the Laplace-Beltrami operator on , is the critical Sobolev exponent, and is a small parameter. The problem can be reduced to a finite dimensional study which is performed with Morse theory.
Some functorial properties of microlocalization for 𝓓-modules
Some generic properties of nonlinear second order diffusional type problem
We are interested of the Newton type mixed problem for the general second order semilinear evolution equation. Applying Nikolskij’s decomposition theorem and general Fredholm operator theory results, the present paper yields sufficient conditions for generic properties, surjectivity and bifurcation sets of the given problem.
Some Gradient Estimates on Covering Manifolds
Let M be a complete Riemannian manifold which is a Galois covering, that is, M is periodic under the action of a discrete group G of isometries. Assuming that G has polynomial volume growth, we provide a new proof of Gaussian upper bounds for the gradient of the heat kernel of the Laplace operator on M. Our method also yields a control on the gradient in case G does not have polynomial growth.
Some heat operators on
Some new conformal covariants.