The aim of this paper is to study (regional) fractional Poincaré type inequalities on unbounded domains satisfying the finite ball condition. Both existence and non results regional inequality are established depending various conditions range \begin{document}$ s \in (0,1) $\end{document}. The best consta...

A coupled Legendre-Laguerre spectral element method is proposed for the Stokes and Navier-Stokes equations in unbounded domains. The method combines advantages of the high accuracy of the Laguerre-spectral method for unbounded domains and the geometric flexibility of the spectral-element method. Rigorous stability and error analysis for the Stokes problem is carried out. Numerical results indic...

Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X)$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X)$ is the space of all $finmathcal{H}(Omega_X)$ for which $$|f(x)|leqslant C omega(r_{Omega_X}(x)),quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the M...

In its full generality, a time domain can be defined as a set of temporal individuals connected by a set of temporal relations. Different choices for the temporal individuals and/or the temporal relations give rise to different temporal ontologies. In the database context, the most common temporal ontology takes time instants (equivalently, points or moments) as the temporal individuals and a l...

We introduce simple tools from geometric convexity to analyze capturetype (or “Lion and Man”) pursuit problems in unbounded domains. The main result is a necessary and sufficient condition for eventual capture in equal-speed discrete-time multi-pursuer capture games on convex Euclidean domains of arbitrary dimension and shape. This condition is presented in terms of recession sets in unit tange...

The initial temperature of a heat conductor is zero and its boundary temperature is kept equal to one at each time. The conductor contains a stationary isothermic surface, that is, an invariant spatial level surface of the temperature. In a previous paper, we proved that, if the conductor is bounded, then it must be a ball. Here, we prove that the boundary of the conductor is either a hyperplan...

In this paper, we introduce an adaptive wavelet method for operator equations on unbounded domains. We use wavelet bases on R to equivalently express the operator equation in terms of a well-conditioned discrete problem on sequence spaces. By realizing an approximate adaptive operator application also for unbounded domains, we obtain a scheme that is convergent at an asymptotically optimal rate...

with a continuous function a and a subcritical growth function g. This type of equation includes the Makutuma equation, when a(|x|) = 1/(1 + |x|2) and g(s) = |s|p−1s, with 1 < p < 2∗ − 1 = (N + 2)/(N − 2), which appears in astrophysics and scalar curvature equations on RN (see, e.g., [15, 17, 18]) In [16] Munyamarere and Willem obtained a result of multiplicity of nodal solutions for these equa...

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi-explicit representation formulas via operatorvalued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the larg...