共查询到20条相似文献,搜索用时 46 毫秒
1.
The boundary value problems for linear and nonlinear degenerate differential-operator equations in Banach-valued Besov spaces are studied. Several conditions for the separability of linear elliptic problems are given. Moreover, the positivity and the analytic semigroup properties of associated differential operators are obtained. By using these results, the maximal regularity of degenerate boundary value problems for nonlinear differential-operator equations is derived. As applications, boundary value problems for infinite systems of degenerate equations in Besov spaces are studied. 相似文献
2.
Stephan Dahlke 《manuscripta mathematica》1998,95(1):59-77
This paper is concerned with some theoretical foundations for adaptive numerical methods for elliptic boundary value problems.
The approximation order that can be achieved by such an adaptive method is determined by certain Besov regularity of the weak
solution. We study Besov regularity for second order elliptic problems in bounded domains in ℝ
d
. The investigations are based on intermediate Schauder estimates and on some potential theoretic framework. Moreover, we
use characterizations of Besov spaces by wavelet expansions.
This work has been supported by the Deutsche Forschungsgemeinschaft (Da 360/1-1) 相似文献
3.
V. S. Guliyev Zhijian Wu 《分析论及其应用》2005,21(2):143-156
We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included. 相似文献
4.
Jon Johnsen 《偏微分方程通讯》2013,38(10):1729-1787
The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type are shown to admit this via exact paralinearization. The parametrices give regularity properties under weak conditions; improvements in subdomains result from pseudo-locality of type 1,1-operators. The framework encompasses a broad class of boundary problems in Hölder and L p -Sobolev spaces (and also Besov and Lizorkin–Triebel spaces). The Besov analyses of homogeneous distributions, tensor products and halfspace extensions have been revised. Examples include the von Karman equation. 相似文献
5.
This paper is concerned with the construction of biorthogonal wavelet bases on n-dimensional cubes which provide Riesz bases for Sobolev and Besov spaces with homogeneous Dirichlet boundary conditions on any desired selection of boundary facets. The essential point is that the primal and dual wavelets satisfy corresponding complementary boundary conditions. These results form the key ingredients of the construction of wavelet bases on manifolds [DS2] that have been developed for the treatment of operator equations of positive and negative order. 相似文献
6.
This study focuses on non-local boundary value problems (BVP) for elliptic differential-operator equations (DOE) defined in Banach-valued Besov (B) spaces. Here equations and boundary conditions contain certain parameters. This study found some conditions that guarantee the maximal regularity and fredholmness in Banach-valued B-spaces uniformly with respect to these parameters. These results are applied to non-local boundary value problems for a regular elliptic partial differential equation with parameters on a cylindrical domain to obtain algebraic conditions that guarantee the same properties. 相似文献
7.
本文利用Litterwood-Palay分解及Besov空间理论研究了C^∞-区域上具非光滑系数的二阶椭圆方程边值问题的Besov正则性问题。 相似文献
8.
O. Chkadua 《Georgian Mathematical Journal》1995,2(2):111-122
The existence and uniqueness of solutions of the boundary-contact problem of elasticity for homogeneous anisotropic media with a contact on some part of their boundaries are investigated in the Besov and Bessel potential classes using the methods of the potential theory and the theory of pseudodifferential equations on manifolds with boundary. The smoothness of the solutions obtained is studied. 相似文献
9.
The dirichlet problem in lipschitz domains for higher order elliptic systems with rough coefficients
Vladimir. Maz’ya Marius Mitrea Tatyana Shaposhnikova 《Journal d'Analyse Mathématique》2010,110(1):167-239
We study the Dirichlet problem, in Lipschitz domains and with boundary data in Besov spaces, for divergence form strongly
elliptic systems of arbitrary order with bounded, complex-valued coefficients. A sharp corollary of our main solvability result
is that the operator of this problem performs an isomorphism between weighted Sobolev spaces when its coefficients and the
unit normal of the boundary belong to the space VMO. 相似文献
10.
In this paper, we define boundary single and double layer potentials for Laplace’s equation in certain bounded domains with
d-Ahlfors regular boundary, considerably more general than Lipschitz domains. We show that these layer potentials are invertible
as mappings between certain Besov spaces and thus obtain layer potential solutions to the regularity, Neumann, and Dirichlet
problems with boundary data in these spaces. 相似文献
11.
Reinhard Hochmuth 《分析论及其应用》2002,18(1):1-25
This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1 ] are chosen as a starting point for characterizations of functions in Besov spaces B , (0,1) with 0<σ<∞ and (1+σ)-1<τ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results. 相似文献
12.
O. O. Chkadua 《Mathematische Nachrichten》1995,172(1):49-64
The existence and uniqueness of solutions of the nonclassical boundary-contact problems (i.e., problems with a contact on some part of the boundaries) of elasticity for homogeneous anisotropic media are investigated in Besov and Bessel potential spaces using methods of potential theory and the theory of pseudodifferential equations on manifolds with boundary. The smoothness of the solutions obtained is studied. 相似文献
13.
Prof. Alf Jonsson 《manuscripta mathematica》1991,71(1):121-152
The trace to the boundary of a domain Ω of functions in Besov spaces and Sobolev spaces defined in Ω is characterized, in
the case when the boundary has singularities of a certain type. 相似文献
14.
We are concerned with the numerical treatment of boundary integral equations by the adaptive wavelet boundary element method. In particular, we consider the second kind Fredholm integral equation for the double layer potential operator on patchwise smooth manifolds contained in ?3. The corresponding operator equations are treated by adaptive implementations that are in complete accordance with the underlying theory. The numerical experiments demonstrate that adaptive methods really pay off in this setting. The observed convergence rates fit together very well with the theoretical predictions based on the Besov regularity of the exact solution. 相似文献
15.
《数学物理学报(B辑英文版)》2016,(3)
In this paper,we prove the existence of global classical solutions to time-dependent Ginzburg-Landau(TDGL) equations.By the properties of Besov and Sobolev spaces,together with the energy method,we establish the global existence and uniqueness of classical solutions to the initial boundary value problem for time-dependent Ginzburg-Landau equations. 相似文献
16.
We consider the Dirichlet problem for Poisson's equation on a nonconvex plane polygonal domain . New regularity estimates for its solution in terms of Besov and Sobolev norms of fractional order are proved. The analysis is based on new interpolation results and multilevel representations of norms on Sobolev and Besov spaces. The results can be extended to a large class of elliptic boundary value problems. Some new sharp finite element error estimates are deduced.
17.
Reinhard Hochmuth 《逼近论及其应用》2002,18(1):1-25
This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besov spaces B r,r 6 (0.1) with 0<σ<∞ and (1+σ)−1相似文献
18.
Mirela Kohr Massimo Lanza de Cristoforis Wolfgang L. Wendland 《Potential Analysis》2013,38(4):1123-1171
The purpose of this paper is to use a layer potential analysis and the Leray–Schauder degree theory to show an existence result for a nonlinear Neumann–transmission problem corresponding to the Stokes and Brinkman operators on Euclidean Lipschitz domains with boundary data in L p spaces, Sobolev spaces, and also in Besov spaces. 相似文献
19.
Some assertions on free interpolation in spaces of functions analytic in the unit disk with boundary values from the Besov classes B p o (T (1?p<+∞,T is the unit circle) are formulated. 相似文献
20.
O. Chkadua 《Mathematische Nachrichten》1997,188(1):23-48
n — Dimensional (n ≥ 2) boundary-contact problems of statics of the elasticity theory for homogeneous anisotropic media are investigated when the contact of two bounded domains occurs from the outside on some part of boundaries with mixed boundary conditions. Theorems on the existence and uniqueness of solutions of boundary-contact problems in Besov and Bessel potential spaces are obtained. The smoothness of solutions is studied in closed domains occupied by elastic media. 相似文献