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1.
Recently Korevaar and Schoen developed a Sobolev theory for maps from smooth (at least ) manifolds into general metric spaces by proving that the weak limit of appropriate average difference quotients is well
behaved. Here we extend this theory to functions defined over Lipschitz manifold. As an application we then prove an existence
theorem for harmonic maps from Lipschitz manifolds to NPC metric spaces.
Received December 6, 1996 / Accepted March 4, 1997 相似文献
2.
JoseM.Roriguez VenancioAlvarez 《逼近论及其应用》2002,18(2):1-32
We present a definition of general Sobolev spaces with respect to arbitrary measures ,W^k,p(Ω,μ) for 1≤p≤∞,In[RARP] we proved that these spaces are complete under very light conditions.Now we prove that if we consider certain general types of measures,then Cc^∞(R) is dense in these spaces,As an application to Sobolev orthogonal polynomials,we study the boundedness of the multiplication poerator,THis gives an estimation of the zeroes of Sobolev orthogonal polynomials. 相似文献
3.
We show that there exists a natural approach version of the topological Vietoris hyperspace construction [16], [17] which has several advantages over the topological version. In the first place the important structural fact that the Vietoris construction can now also be considered, not only for topological but also intrinsically for metric spaces, but equally important in the second place the fact that we can considerably strengthen fundamental classic results. In this paper we mainly pay attention to properties concerning or involving compactness. As main results, in the first place we prove that it is not merely compactness of the Vietoris hyperspace which is equivalent to compactness of the original space [3] but that actually in the approach setting the indices of compactness [7], [8], [9], [10] numerically completely coincide. In the second place the well-known result [3], [4], [15] which says that if the original space is compact metric then the Vietoris topology is metrizable by the Hausdorff metric gets strengthened in the sense that in the approach setting under the same conditions the Vietoris approach structure actually coincides with the Hausdorff metric. Classic results follow as easy corollaries. Besides these main results we also draw attention to the good functorial relationship between the Vietoris approach structures and the associated topologies. 相似文献
4.
We present a definition of general Sobolev spaces with respect to arbitrary measures, Wh,p (Ω,μ) for 1 ≤p≤∞. In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then Cc∞ (R) is dense in thee spaces. As an application to Sobolev orthogonal polynomials, we study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials. 相似文献
5.
S. Kumar 《Acta Mathematica Hungarica》2008,118(1-2):9-28
We prove expansion mappings theorems in various spaces i.e., metric spaces, generalized metric spaces, probabilistic metric
spaces and fuzzy metric spaces, which generalize the results of various authors like Daffer and Kaneko [11], Ahmad, Ashraf
and Rhoades [1], Vasuki [38], Rhoades [31] and Wang, Li, Gao and Iseki [40] etc.
In the memory of 65th birthday anniversary of his Father Late Sh. Ram Phool Sharma 相似文献
6.
Intuitionistic fuzzy metric spaces 总被引:8,自引:0,他引:8
Using the idea of intuitionistic fuzzy set due to Atanassov [Intuitionistic fuzzy sets. in: V. Sgurev (Ed.), VII ITKR's Session, Sofia June, 1983; Fuzzy Sets Syst. 20 (1986) 87], we define the notion of intuitionistic fuzzy metric spaces as a natural generalization of fuzzy metric spaces due to George and Veeramani [Fuzzy Sets Syst. 64 (1994) 395] and prove some known results of metric spaces including Baire's theorem and the Uniform limit theorem for intuitionistic fuzzy metric spaces. 相似文献
7.
D. Turkoglu C. Alaca Y. J. Cho C. Yildiz 《Journal of Applied Mathematics and Computing》2006,22(1-2):411-424
The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck’s common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant’s theorem ([21]). 相似文献
8.
In this paper we prove some fixed points results on cone metric spaces for maps satisfying general contractive type conditions. Among other things, we extend some results of Nguyen [11] from metric spaces to cone metric spaces. The example is included. 相似文献
9.
Jacek Jachymski 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(3):768-774
We establish a geometric lemma giving a list of equivalent conditions for some subsets of the plane. As its application, we get that various contractive conditions using the so-called altering distance functions coincide with classical ones. We consider several classes of mappings both on metric spaces and ordered metric spaces. In particular, we show that unexpectedly, some very recent fixed point theorems for generalized contractions on ordered metric spaces obtained by Harjani and Sadarangani [J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. 72 (2010) 1188-1197], and Amini-Harandi and Emami [A. Amini-Harandi, H. Emami A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. 72 (2010) 2238-2242] do follow from an earlier result of O’Regan and Petru?el [D. O’Regan and A. Petru?el, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. 341 (2008) 1241-1252]. 相似文献
10.
Guozhen Lu 《数学学报(英文版)》2000,16(3):405-444
This paper consists of three main parts. One of them is to develop local and global Sobolev interpolation inequalities of any higher order for the nonisotropic Sobolev spaces on stratified nilpotent Lie groups. Despite the extensive research after Jerison's work [3] on Poincaré-type inequalities for Hörmander's vector fields over the years, our results given here even in the nonweighted case appear to be new. Such interpolation inequalities have crucial applications to subelliptic or parabolic PDE's involving vector fields. The main tools to prove such inqualities are approximating the Sobolev functions by polynomials associated with the left invariant vector fields on ?. Some very usefull properties for polynomials associated with the functions are given here and they appear to have independent interests in their own rights. Finding the existence of such polynomials is the second main part of this paper. Main results of these two parts have been announced in the author's paper in Mathematical Research Letters [38].The third main part of this paper contains extension theorems on anisotropic Sobolev spaces on stratified groups and their applications to proving Sobolev interpolation inequalities on (?,δ) domains. Some results of weighted Sobolev spaces are also given here. We construct a linear extension operator which is bounded on different Sobolev spaces simultaneously. In particular, we are able to construct a bounded linear extension operator such that the derivatives of the extended function can be controlled by the same order of derivatives of the given Sobolev functions. Theorems are stated and proved for weighted anisotropic Sobolev spaces on stratified groups. 相似文献
11.
A. Roldán J. Martínez-Moreno C. Roldán 《Journal of Mathematical Analysis and Applications》2012,396(2):536-545
In this paper we propose a notion of coincidence point between mappings in any number of variables and we prove some existence and uniqueness fixed point theorems for nonlinear mappings verifying different kinds of contractive conditions and defined on partially ordered metric spaces. These theorems extend and clarify very recent results that can be found in [T. Gnana-Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7)(2006) 1379–1393], [V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 4889–4897] and [M. Berzig, B. Samet, An extension of coupled fixed point’s concept in higher dimension and applications, Comput. Math. Appl. 63 (8) (2012) 1319–1334]. 相似文献
12.
G.C.L. Brümmer 《Topology and its Applications》2006,153(16):3101-3112
We develop a bicompletion theory for the category Ap0 of T0 approach spaces in the sense of Lowen [R. Lowen, Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad, Oxford University Press, Oxford, 1997], which extends the completion theory obtained in [R. Lowen, K. Robeys., Completions of products of metric spaces, Quart. J. Math. Oxford 43 (1991) 319-338] for the subcategory of Hausdorff uniform approach spaces. Moreover, we prove it to be firmly epireflective (in the sense of [G.C.L. Brümmer, E. Giuli, A categorical concept of completion of objects, Comment. Math. Univ. Carolin. 33 (1992) 131-147]) with respect to a certain morphism class of dense embeddings. 相似文献
13.
《Journal of Approximation Theory》2003,120(2):185-216
The density of polynomials is straightforward to prove in Sobolev spaces Wk,p((a,b)), but there exist only partial results in weighted Sobolev spaces; here we improve some of these theorems. The situation is more complicated in infinite intervals, even for weighted Lp spaces; besides, in the present paper we have proved some other results for weighted Sobolev spaces in infinite intervals. 相似文献
14.
Sina Degenfeld-Schonburg 《Rendiconti del Circolo Matematico di Palermo》2013,62(3):409-425
A bounded linear operator is called multiplier with respect to Jacobi polynomials if and only if it commutes with all Jacobi translation operators on $[-1,1]$ . Multipliers on homogeneous Banach spaces on $[-1,1]$ determined by the Jacobi translation operator are introduced and studied. First we prove four equivalent characterizations of a multiplier for an arbitrary homogeneous Banach spaces $B$ on $[-1,1]$ . One of them implies the existence of an algebra isomorphism from the set of all multipliers on $B$ into the set of all pseudomeasures. Further, we study multipliers on specific examples of homogeneous Banach spaces on $[-1,1]$ . Amongst others, multipliers on the Wiener algebra, on the Beurling space and on Sobolev spaces are analyzed. We obtain that the multiplier spaces of the Wiener algebra, the Beurling space and of all Sobolev spaces are isometric isomorphic to each other. Furthermore, these multiplier spaces are all isometric isomorphic to the set of all pseudomeasures. 相似文献
15.
This article is concerned with constructions of biorthogonal basis of compactly supported wavelets in Sobolev spaces of integer
order. Using techniques of [1] and [2], the results presented here generalize to Sobolev spaces some constructions of Cohen
et al. [7] and Chui and Wang [5] established in L2(ℝ). 相似文献
16.
Zhaoxi Wang 《分析论及其应用》2009,25(1):92-100
The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a “chain of function spaces“ over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields. 相似文献
17.
A metric space is indivisible if for any partition of it into finitely many pieces one piece contains an isometric copy of the whole space. Continuing our investigation of indivisible metric spaces [C. Delhommé, C. Laflamme, M. Pouzet, N. Sauer, Divisibility of countable metric spaces, European J. Combin. 28 (2007) 1746-1769], we show that a countable ultrametric space is isometrically embeddable into an indivisible ultrametric space if and only if it does not contain a strictly increasing sequence of balls. 相似文献
18.
We discuss the potential theory related to the variational capacity and the Sobolev capacity on metric measure spaces. We prove our results in the axiomatic framework of [17].46E35, 31C15, 31C45 相似文献
19.
Víctor Domínguez Norbert Heuer 《Journal of Computational and Applied Mathematics》2011,235(12):3481-3501
In this paper we study the Hilbert scales defined by the associated Legendre functions for arbitrary integer values of the parameter. This problem is equivalent to studying the left-definite spectral theory associated to the modified Legendre equation. We give several characterizations of the spaces as weighted Sobolev spaces and prove identities among the spaces corresponding to the lower regularity index. 相似文献
20.
《Journal of Computational and Applied Mathematics》1998,89(2):213-217
We prove a remarkable property for the coefficients of the linear differential operator of finite order found in [2], having Sobolev type Laguerre polynomials as eigenfunctions. 相似文献