Some uniqueness results for Bernoulli interior free-boundary problems in convex domains.
Some weighted Hardy-type inequalities on anisotropic Heisenberg groups.
Source type positive solutions of nonlinear parabolic inequalities
Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs
The numerical approximation of parametric partial differential equations is a computational challenge, in particular when the number of involved parameter is large. This paper considers a model class of second order, linear, parametric, elliptic PDEs on a bounded domain D with diffusion coefficients depending on the parameters in an affine manner. For such models, it was shown in [9, 10] that under very weak assumptions on the diffusion coefficients, the entire family of solutions to such equations...
Spatial smoothness of the stationary solutions of the 3D Navier-Stokes equations.
Spazi BV e di Nikolskii e applicazioni al problema di Stefan
Questa Nota è dedicata a mettere in evidenza alcune proprietà degli spazi delle funzioni a variazione limitata e degli spazi di Nikolskii ed , ( ), che non mi risulta siano già state esposte nella forma generale qui enunciata, quali la non separabilità, l'essere il duale di uno spazio di Banach separabile, la convergenza e la compattezza debole in e le loro applicazioni al classico problema di Stefan bifase.
SPDEs with coloured noise: Analytic and stochastic approaches
We study strictly parabolic stochastic partial differential equations on , d ≥ 1, driven by a Gaussian noise white in time and coloured in space. Assuming that the coefficients of the differential operator are random, we give sufficient conditions on the correlation of the noise ensuring Hölder continuity for the trajectories of the solution of the equation. For self-adjoint operators with deterministic coefficients, the mild and weak formulation of the equation are related, deriving...
Spectral properties of non-local uniformly-elliptic operators.
Spectral statistics for random Schrödinger operators in the localized regime
We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy in the localized phase. Assume the density of states function is not too flat near . Restrict it to some large cube . Consider now , a small energy interval centered at that asymptotically contains infintely many eigenvalues when the volume of the cube grows to infinity. We prove that, with probability one in the large volume...
Spline collocation for strongly elliptic equations on the torus.
Spreading and vanishing in nonlinear diffusion problems with free boundaries
We study nonlinear diffusion problems of the form with free boundaries. Such problems may be used to describe the spreading of a biological or chemical species, with the free boundary representing the expanding front. For special of the Fisher-KPP type, the problem was investigated by Du and Lin [DL]. Here we consider much more general nonlinear terms. For any which is and satisfies , we show that the omega limit set of every bounded positive solution is determined by a stationary solution....
Stabilité des solitons de l’équation de Landau-Lifshitz à anisotropie planaire
Cet exposé présente plusieurs résultats récents quant à la stabilité des solitons sombres de l’équation de Landau-Lifshitz à anisotropie planaire, en particulier, quant à la stabilité orbitale des trains (bien préparés) de solitons gris [16] et à la stabilité asymptotique de ces mêmes solitons [2].
Stability and continuous dependence of solutions of one-phase Stefan problems for semilinear parabolic equations.
Stability and saddle-point property for a linear autonomous functional parabolic equation
Stability estimates for a linearized Muskat problem
Stability estimates for an inverse problem for the linear Boltzmann equation.
In this paper we consider the inverse problem of recovering the total extinction coefficient and the collision kernel for the time-dependent Boltzmann equation via boundary measurements. We obtain stability estimates for the extinction coefficient in terms of the albedo operator and also an identification result for the collision kernel.
Stability estimates of an inverse problem for the stationary transport equation
Stability for approximation methods of the one-dimensional Kobayashi-Warren-Carter system
A one-dimensional version of a gradient system, known as “Kobayashi-Warren-Carter system”, is considered. In view of the difficulty of the uniqueness, we here set our goal to ensure a “stability” which comes out in the approximation approaches to the solutions. Based on this, the Main Theorem concludes that there is an admissible range of approximation differences, and in the scope of this range, any approximation method leads to a uniform type of solutions having a certain common features. Further,...
Stability of a numerical method for solving the 3 D inverse scattering problem with fixed energy data.
Stability of contact discontinuities under perturbations of bounded variation