Search results for "A domain"
showing 10 items of 37 documents
CVBEM application to a novel potential function providing stress field and twist rotation at once
2013
AbstractIn this paper, complex variable boundary element method (CVBEM) is used for the solution of de Saint-Venant’s torsion problem in homogenous isotropic elastic beams with a generic cross section, considering a complex potential function related to the stress field. Generally, CVBEM, when used for torsion problems, leads to evaluation of the stress field divided by the twist rotation. The latter has been evaluated by performing a domain integral. In this paper, taking advantage of the aforementioned potential function, it is possible, by applying CVBEM, to evaluate the complete stress distribution and the twist rotation of the cross section and the torsional stiffness factor, performin…
Weighted pointwise Hardy inequalities
2009
We introduce the concept of a visual boundary of a domain �¶ �¼ Rn and show that the weighted Hardy inequality �¶ |u|pd�¶ �A.p C �¶ |�Þu|pd�¶ �A, where d�¶(x) = dist(x, �Ý�¶), holds for all u �¸ C �� 0 (�¶) with exponents �A < �A0 when the visual boundary of �¶ is sufficiently large. Here �A0 = �A0(p, n, �¶) is explicit, essentially sharp, and may even be greater than p . 1, which is the known bound for smooth domains. For instance, in the case of the usual von Koch snowflake domain the sharp bound is shown to be �A0 = p . 2 + �E, with �E = log 4/ log 3. These results are based on new pointwise Hardy inequalities.
Locally tame plane polynomial automorphisms
2010
Abstract For automorphisms of a polynomial ring in two variables over a domain R , we show that local tameness implies global tameness provided that every 2-generated locally free R -module of rank 1 is free. We give examples illustrating this property.
Notions of Dirichlet problem for functions of least gradient in metric measure spaces
2019
We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a (1, 1)-Poincaré inequality. Since one of the two notions is not amenable to the direct method of the calculus of variations, we construct, based on an approach of Juutinen and Mazón-Rossi–De León, solutions by considering the Dirichlet problem for p-harmonic functions, p>1, and letting p→1. Tools developed and used in this paper include the inner perimeter measure of a domain. Peer reviewed
On BLD-mappings with small distortion
2021
We show that every $$L$$ -BLD-mapping in a domain of $$\mathbb {R}^{n}$$ is a local homeomorphism if $$L < \sqrt{2}$$ or $$K_I(f) < 2$$ . These bounds are sharp as shown by a winding map.
Jacobian of weak limits of Sobolev homeomorphisms
2016
Abstract Let Ω be a domain in ℝ n {\mathbb{R}^{n}} , where n = 2 , 3 {n=2,3} . Suppose that a sequence of Sobolev homeomorphisms f k : Ω → ℝ n {f_{k}\colon\Omega\to\mathbb{R}^{n}} with positive Jacobian determinants, J ( x , f k ) > 0 {J(x,f_{k})>0} , converges weakly in W 1 , p ( Ω , ℝ n ) {W^{1,p}(\Omega,\mathbb{R}^{n})} , for some p ⩾ 1 {p\geqslant 1} , to a mapping f. We show that J ( x , f ) ⩾ 0 {J(x,f)\geqslant 0} a.e. in Ω. Generalizations to higher dimensions are also given.
The space H(Ω,(zj)) of holomorphic functions
2008
Abstract Let Ω be a domain in C n . Let H ( Ω ) be the linear space over C of the holomorphic functions in Ω, endowed with the compact-open topology. Let ( z j ) be a sequence in Ω without adherent points in Ω. In this paper, we define the space H ( Ω , ( z j ) ) and some of its linear topological properties are studied. We also show that, for some domains of holomorphy Ω and some sequences ( z j ) , the non-zero elements of H ( Ω , ( z j ) ) cannot be extended holomorphically outside Ω. As a consequence, we obtain some characterizations of the domains of holomorphy in C n .
Approximation of W1, Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian
2018
Abstract Let Ω ⊂ R n , n ≥ 4 , be a domain and 1 ≤ p [ n / 2 ] , where [ a ] stands for the integer part of a. We construct a homeomorphism f ∈ W 1 , p ( ( − 1 , 1 ) n , R n ) such that J f = det D f > 0 on a set of positive measure and J f 0 on a set of positive measure. It follows that there are no diffeomorphisms (or piecewise affine homeomorphisms) f k such that f k → f in W 1 , p .
Anisotropic Sobolev homeomorphisms
2011
Let › ‰ R 2 be a domain. Suppose that f 2 W 1;1 loc (›;R 2 ) is a homeomorphism. Then the components x(w), y(w) of the inverse f i1 = (x;y): › 0 ! › have total variations given by jryj(› 0 ) = › fl fl @f fl fl dz; jrxj(› 0 ) = › fl fl @f @y fl fl dz:
SEAL: A Domain-Specific Language for Novice Wireless Sensor Network Programmers
2013
A lot of the prospective wireless sensor network users are novice programmers. Their experience in general-purpose programming languages is either limited or completely nonexistent. There are both financial and scientific incentives to empower these users and allow them to write sensor network applications on their own, rather than having to rely on a qualified computer science professional. We present SEAL, a sensor network programming language designed for novice programmers. SEAL manages to avoid computer science concepts that are hard to grasp for novices, while remaining suitable for typical sensor network application scenarios. The language is extensible in application-specific way, h…