摘要:

Let 𝔎 be a sheaf of continuous real-valued functions on a domain. If 𝔎 satisfies the axioms for a nonlinear potential theory, then we call the elements of 𝔎(U) forU⊂Ω open𝔎-harmonic onU.We define the class 𝔖(U) of 𝔎-superharmonic functions onUand characterize best uniform approximations to continuous functions by elements of 𝔖(U) ∩C(Ʉ).

ISSN:0163-0563    

DOI:10.1080/01630569208816457

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

A free boundary value problem is considered modeling solidification of a liquid by making use of the phase field approach as it was introduced by G. Caginalp [1] and others. Existence and uniqueness is proved as well as stability under mild assumptions. But the main goal of this paper is to establish results for the distributed optimal control of the phase field equations. Besides the existence of an optimal control necessary optimality conditions will be proved and some uniqueness results will be obtained.

ISSN:0163-0563    

DOI:10.1080/01630569208816458

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

In this paper we investigate the uniqueness of best approximation of continuous functions on [-aa] in the norm, by elements of Haar andA-spaces. It turns out that the size of the interval is crucial for uniqueness. In most cases we shall determine the exact set of a's for which uniqueness holds. We also show that in the case whenr= 1 the approximation by Haar spaces yields uniqueness for everya.

ISSN:0163-0563    

DOI:10.1080/01630569208816459

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

The existence of a solution of a hemivariational inequality is proved and the full discretization of it is discussed. Then we study the approximation of the optimal control problem, the state relation of which is done by the hemivariational inequality.

ISSN:0163-0563    

DOI:10.1080/01630569208816460

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

Schock (1985) has considered the convergence properties of various Galerkin-like methods for the approximate solution of the operator equation of the second kindx - Tx = y, whereTis a bounded linear operator on a Banach spaceX, andxandybelong toX, and proved that the classical Galerkin method and in certain cases, the iterated Galerkin method are arbitrarily slowly convergent whereas the Kantororich method studied by him is uniformly convergent. It is the purpose of this paper to introduce a general class of approximations methods forx - Tx = ywhich includes the well-known methods of projection and the quadrature methods, and to characterize its uniform convergence, so that an arbitrarily slowly convergent method can be modified to obtain a uniformly convergent method.

ISSN:0163-0563    

DOI:10.1080/01630569208816461

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

We develop methods for constructing sets of points which admit Lagrange and Hermite type interpolation by spaces of bivariate splines on rectangular and triangular partitions which are uniform, in general. These sets are generated by building up a net of lines and by placing points on these lines which satisfy interlacing properties for univariate spline spaces.

ISSN:0163-0563    

DOI:10.1080/01630569208816462

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

In this paper we study local behavior of optimal solutions of parametric programs in Banach spaces. A general approach to approximation of the original problem by a simpler one is outlined. Under various regularity conditions, Lipschitz continuity and directional differentiability properties of the optimal solutions are derived.

ISSN:0163-0563    

DOI:10.1080/01630569208816463

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

Letand letForfεF, there exist linear wavelet operatorsLk(F, x)which are also distribution functions and where the defining mother wavelet is Φ(x). These approximateF(x)in the-norm. The degree of this approximation is estimated by establishing anLρJackson type inequality.

ISSN:0163-0563    

DOI:10.1080/01630569208816464

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

SupposeVis a subspace ofandhε. For 1 <p< ∞, lethpbe the bestlpapproximation tohby elements ofVElementary proofs are given that limp→∞hpand limp→1hpboth exist.

ISSN:0163-0563    

DOI:10.1080/01630569208816465

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor

摘要:

F. Stummel's notion of discrete approximation and one of its possible concretizations are used. The concepts of consistency, closedness, stability (BR-stability) and regularity (B-regularity) of the sequences of operators at some pointvare considered. The behavior of the sequences of the solutions of approximating equations (sequences ofo-solutions) is studied.

ISSN:0163-0563    

DOI:10.1080/01630569208816466

出版商:Marcel Dekker, Inc.    

年代:1992

数据来源: Taylor