Stochastic processes and antiderivational equations on non-Archimedean manifolds.
Stochastic processes on totally disconnected topological groups.
Stochastic Taylor expansions and heat kernel asymptotics
These notes focus on the applications of the stochastic Taylor expansion of solutions of stochastic differential equations to the study of heat kernels in small times. As an illustration of these methods we provide a new heat kernel proof of the Chern–Gauss–Bonnet theorem.
Stokes' formula for singular chains in a differential space of finite dimension
Stokes' phenomenon; smoothing a victorian discontinuity
Stratification of minimal surfaces, mean curvature flows, and harmonic maps.
Stratification theory from the Newton polyhedron point of view
Recently, T. Fukui and L. Paunescu introduced a weighted version of the -regularity condition and Kuo’s ratio test condition. In this approach, we consider the - regularity condition and -regularity related to a Newton filtration.
Stratifications of polynomial spaces
In the paper we construct some stratifications of the space of monic polynomials in real and complex cases. These stratifications depend on properties of roots of the polynomials on some given semialgebraic subset of R or C. We prove differential triviality of these stratifications. In the real case the proof is based on properties of the action of the group of interval exchange transformations on the set of all monic polynomials of some given degree. Finally we compare stratifications corresponding...
Stratifications of teardrops
Teardrops are generalizations of open mapping cylinders. We prove that the teardrop of a stratified approximate fibration X → Y × ℝ with X and Y homotopically stratified spaces is itself a homotopically stratified space (under mild hypothesis). This is applied to manifold stratified approximate fibrations between manifold stratified spaces in order to establish the realization part of a previously announced tubular neighborhood theory.
Stratified semiconcave control-Lyapunov functions and the stabilization problem
Stratified Whitney jets and tempered ultradistributions on the subanalytic site
In this paper we introduce the sheaf of stratified Whitney jets of Gevrey order on the subanalytic site relative to a real analytic manifold . Then, we define stratified ultradistributions of Beurling and Roumieu type on . In the end, by means of stratified ultradistributions, we define tempered-stratified ultradistributions and we prove two results. First, if is a real surface, the tempered-stratified ultradistributions define a sheaf on the subanalytic site relative to . Second, the tempered-stratified...
Strengthening upper bound for the number of critical levels of nonlinear functionals
Strichartz estimates for the wave equation on manifolds with boundary
Strichartz inequalities for Lipschitz metrics on manifolds and nonlinear Schrödinger equation on domains
We prove wellposedness of the Cauchy problem for the nonlinear Schrödinger equation for any defocusing power nonlinearity on a domain of the plane with Dirichlet boundary conditions. The main argument is based on a generalized Strichartz inequality on manifolds with Lipschitz metric.
Strichartz inequalities for the Schrödinger equation with the full Laplacian on the Heisenberg group
We prove Strichartz inequalities for the solution of the Schrödinger equation related to the full Laplacian on the Heisenberg group. A key point consists in estimating the decay in time of the norm of the free solution; this requires a careful analysis due also to the non-homogeneous nature of the full Laplacian.
Strict differentiability via differentiability
Strong boundary values : independence of the defining function and spaces of test functions
The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.
Strong density for higher order Sobolev spaces into compact manifolds
Given a compact manifold , an integer and an exponent , we prove that the class of smooth maps on the cube with values into is dense with respect to the strong topology in the Sobolev space when the homotopy group of order is trivial. We also prove density of maps that are smooth except for a set of dimension , without any restriction on the homotopy group of .
Strong infinitesimal linearity, with applications to strong difference and affine connections
Strong Rigidity of Irreducible Quotients of Polydiscs of Finite Volume.