Related papers: Inf-sup estimates for the Stokes problem in a peri…
The Lipschitz constant of a response surface function upper bounds the sensitivity of a dependent variable to changes in the independent ones. Traditionally, such constants have found much implicit and abstract use in mathematically…
For a hyperbolic map f on a saddle type fractal Lambda with self-intersections, the number of f- preimages of a point x in Lambda may depend on x. This makes estimates of the stable dimensions more difficult than for diffeomorphisms or for…
For Stokes waves in finite depth within the neighbourhood of the Benjamin-Feir stability transition, there are two families of periodic waves, one modulationally unstable and the other stable. In this paper we show that these two families…
We study the smoothness of the upper and lower value functions of stochastic differential games in the framework of time-homogeneous (possibly degenerate) diffusion processes in a domain, under the assumption that the diffusion, drift and…
Recently, Hairer et. al (2012) showed that there exist SDEs with infinitely often differentiable and globally bounded coefficient functions whose solutions fail to be locally Lipschitz continuous in the strong L^p-sense with respect to the…
We propose solution of the problem of the mean square optimal estimation of linear functionals which depend on the unobserved values of a continuous time stochastic process with periodically correlated increments based on observations of…
We introduce stochastic sequences $\zeta(k)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the…
We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…
We study the problem of reconstructing the Faber--Schauder coefficients of a continuous function $f$ from discrete observations of its antiderivative $F$. For instance, this question arises in financial mathematics when estimating the…
We consider a sequence of finite irreducible Markov chains with exponentially small transition rates: the transition graph is a fixed, finite, strongly connected directed graph; the transition rates decay exponentially on a paramenter N…
We consider transformations preserving a contracting foliation, such that the associated quotient map satisfies a Lasota-Yorke inequality. We prove that the associated transfer operator, acting on suitable normed spaces, has a spectral gap…
Nonlinear dynamic systems can be classified into various classes depending on the modeled nonlinearity. These classes include Lipschitz, bounded Jacobian, one-sided Lipschitz (OSL), and quadratically inner-bounded (QIB). Such classes…
We consider the mixed Dirichlet-conormal problem on irregular domains in $\mathbb{R}^d$. Two types of regularity results will be discussed: the $W^{1,p}$ regularity and a non-tangential maximal function estimate. The domain is assumed to be…
The main aim of this paper is to describe the dynamic transitions in flows described by the two-dimensional, barotropic vorticity equation in a periodic zonal channel. In \cite{CGSW03}, the existence of a Hopf bifurcation in this model as…
In this paper we investigate continuity properties of first and second order shape derivatives of functionals depending on second order elliptic PDE's around nonsmooth domains, essentially either Lipschitz or convex, or satisfying a uniform…
A pressure-driven two-layer channel flow of a Newtonian fluid with constant viscosity (top layer) and a fluid with a time-dependent viscosity (bottom layer) is numerically investigated. The bottom layer goes through an aging process in…
In this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier-Stokes equations with viscous coefficient depending on the density and with initial density being discontinuous…
Liv\v{s}ic theorem asserts that, for Anosov diffeomorphisms/flows, a Lipschitz observable is a coboundary if all its Birkhoff sums on every periodic orbits are equal to zero. The transfer function is then Lipschitz. We prove a positive…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…
We consider the class of convex minimization problems, composed of a self-concordant function, such as the $\log\det$ metric, a convex data fidelity term $h(\cdot)$ and, a regularizing -- possibly non-smooth -- function $g(\cdot)$. This…