Let us consider two compact connected and locally connected Hausdorff spaces M , N and two continuous functions φ : M → R, ψ : N → R . In this paper we introduce new pseudodistances between pairs (M,φ) and (N,ψ) associated with reparametrization invariant seminorms. We study the pseudodistance associated with the seminorm ‖φ‖ = maxφ − minφ, denoted by δΛ, and we find a sharp lower bound for it....

The paper deals with a singularly perturbed reaction diffusion model problem. The focus is on reliable a posteriori error estimators for the H1 seminorm that can be applied to anisotropic finite element meshes. A residual error estimator and a local problem error estimator are proposed and rigorously analysed. They are locally equivalent, and both bound the error reliably. Furthermore three mod...

We consider an optimal rearrangement maximization problem involving the fractional Laplace operator ( − Δ ) s , 0 < 1 and Gagliardo-Nirenberg seminorm [ u ] . prove existence of a maximizer, analyze its properties show that it satisfies unstable obstacle equation for some α > = χ { }

Abstract. Numerical solution of one-dimensional elliptic problems is investigated using an averaged discontinuous discretization. The corresponding numerical method can be performed using the favorable properties of the discontinuous Galerkin (dG) approach, while for the average an error estimation is obtained in the H-seminorm. We point out that this average can be regarded as a lower order mo...

Abstract Our aim is to characterize the homogeneous fractional Sobolev–Slobodecki? spaces $$\mathcal {D}^{s,p} (\mathbb {R}^n)$$ D s , p ( R n ) ...

It is well known that finite element solutions for elliptic PDEs with Dirac measures as source terms converge, due to the fact that the solution is not in H1, suboptimal in classical norms. A standard remedy is to use graded meshes, then quasioptimality, i.e., optimal up to a log-factor, for low order finite elements can be recovered, e.g., in the L2-norm. Here we show for the lowest order case...

We study the topological spectrum of a seminormed ring $R$ which we define as space prime ideals $\mathfrak{p}$ such that equals kernel some bounded power-multiplicative seminorm. For any show is quasi-compact sober space. When perfectoid Tate construct natural homeomorphism between and its tilt $R^{\flat}$. As an application, prove integral domain if only domain.

Let I be a finite interval and r ∈ N. Denote by ∆ s + L q the subset of all functions y ∈ L q such that the s-difference ∆ s τ y(·) is nonnegative on I, ∀τ > 0. Further, denote by ∆ s + W r p , the class of functions x on I with the seminorm x (r) L p ≤ 1, such that ∆ s τ x ≥ 0, τ > 0. For s = 3,. .. , r + 1, we obtain two-sided estimates of the shape preserving widths

The convergence rate of a multigrid method for the numerical solution of the Poisson equation on a uniform grid is estimated. The results are independent of the shape of the domain as long as it is convex and polygonal. On the other hand, pollution effects become apparent when the domain contains reentrant corners. To estimate the smoothing of the Gauss-Seidel relaxation, the smoothness is meas...