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.
Some non-linear function theoretic properties of Riemannian manifolds.
We study the appropriate versions of parabolicity stochastic completeness and related Liouville properties for a general class of operators which include the p-Laplace operator, and the non linear singular operators in non-diagonal form considered by J. Serrin and collaborators.
Some progress in conformal geometry.
Some regularity theorems in riemannian geometry
Some remarks on almost-positivity of 's
Per una classe di operatori pseudodifferenziali a caratteristiche multiple vengono date condizioni necessarie e sufficienti per la validità di stime dal basso «ottimali»
Some remarks on gradient estimates for heat kernels.
Some remarks on the heat flow for functions and forms.
Some remarks on the index theorem approach to anomalies
Some remarks on the weak maximum principle.
We obtain a maximum principle at infinity for solutions of a class of nonlinear singular elliptic differential inequalities on Riemannian manifolds under the sole geometrical assumptions of volume growth conditions. In the case of the Laplace-Beltrami operator we relate our results to stochastic completeness and parabolicity of the manifold.
Some Remarks on Transmutation, Scattering Theory, and Special Functions.
Some results on eigenfunctions on symmetric spaces and eigenspace representations.
Some spectral results for the Laplacian on line bundles over Sn.