Related papers: Lebesgue Constants Arising in a Class of Collocati…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
Can graded meshes yield more accurate numerical solution than uniform meshes? A time-dependent nonlocal diffusion problem with a weakly singular kernel is considered using collocation method. For its steady-state counterpart, under the…
A unique set of correction functions for Flux Reconstruction is presented, with there derivation stemming from proving the existence of energy stability in the Lebesgue norm. The set is shown to be incredibly arbitrary with the only union…
We consider divergence form uniformly parabolic SPDEs with bounded and measurable leading coefficients and possibly growing lower-order coefficients in the deterministic part of the equations. We look for solutions which are summable to the…
The general problem of characterizing gas source parameters based on concentration measurements is known to be a difficult task. As many inverse problems, one of the main obstacles for accurate estimation is the non-uniqueness of solution,…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
In this paper, we establish spectral inequalities on measurable sets of positive Lebesgue measure for the Stokes operator, as well as an observability inequalities on space-time measurable sets of positive measure for non-stationary Stokes…
Polynomial reproduction plays a relevant role in deriving error estimates for various approximation schemes. Local reproduction in a quasi-uniform setting is a significant factor in the estimation of error and the assessment of stability…
An error analysis of Runge-Kutta convolution quadrature based on Gauss methods applied to hyperbolic operators is given. The order of convergence relies heavily on the parity of the number of stages, a more favourable situation arising for…
We consider the classical obstacle problem on bounded, connected Lipschitz domains $D \subset \mathbb{R}^n$. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right hand side and the…
The Roche potential is the sum of the gravitational and rotational potentials experienced by a massless body rotating alongside two massive bodies in a circular orbit. The Lagrangian points are five stationary points in the Roche potential.…
For a given $\theta\in (-1,1)$, we find out all parameters $\alpha,\beta\in \{0,1\}$ such that, there exists a linear combination of Jacobi polynomials $J_{n+1}^{(\alpha,\beta)}(x)-C J_{n}^{(\alpha,\beta)}(x)$ which generates a Lobatto…
We consider a process given as the solution of a one-dimensional stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. H\"older continuity of the Lebesgue density of…
In this paper we prove an optimal estimate for the norm of wavelet localization operators with Cauchy wavelet and weight functions that satisfy two constraints on different Lebesgue norms. We prove that multiple regimes arise according to…
We study the problem estimation of classical Lebesgue-Riesz and Grand Lebesgue Norm for the fractional integrals and derivatives for the functions from the classical Lebesgue-Riesz spaces as well as from the modified Besov's spaces.
The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…
We study the stationary points of what is known as the lattice Landau gauge fixing functional in one-dimensional compact U(1) lattice gauge theory, or as the Hamiltonian of the one-dimensional random phase XY model in statistical physics.…
In a $n$-dimensional Lie algebra, random numerical values are assigned by computer to $n(n-1)$ especially selected structure constants. An algorithm is then created, which calculates without ambiguity the remaining constants, obeying the…
We deduce mixed quasi-norm estimates of Lebesgue types on semi-continuous convolutions between sequences and functions which may be periodic or possess a weaker form of periodicity in certain directions. In these directions, the Lebesgue…
Last years there was increasing an interest to the so called function spaces with non-standard growth, known also as variable exponent Lebesgue spaces. For weighted such spaces on homogeneous spaces, we develop a certain variant of Rubio de…