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971.
Jan Harm van der Walt 《Acta Appl Math》2009,106(2):149-176
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion as presented
in Oberguggenberger and Rosinger (Solution of continuous nonlinear PDEs through order completion, North-Holland, Amsterdam,
1994). In particular, spaces of generalized functions are constructed that contain generalized solutions to a large class of systems
of continuous, nonlinear PDEs. In terms of the existence and uniqueness results previously obtained for such systems of equations
(van der Walt, Acta Appl. Math. 103:1–17, 2008), one may interpret the existence of generalized solutions presented here as a regularity result. Furthermore, it is indicated
how the methods developed in this paper may be adapted to solve initial and/or boundary value problems. In particular, we
consider the Navier-Stokes equations in three spacial dimensions, subject to an initial condition on the velocity. In this
regard, we obtain the existence of a generalized solution to a large class of such initial value problems.
相似文献
972.
Let p∈(0,1] and s≥[n(1/p−1)], where [n(1/p−1)] denotes the maximal integer no more than n(1/p−1). In this paper, the authors prove that a linear operator T extends to a bounded linear operator from the Hardy space H
p
(ℝ
n
) to some quasi-Banach space ℬ if and only if T maps all (p,2,s)-atoms into uniformly bounded elements of ℬ.
相似文献
973.
Michael Taylor 《Journal of Geometric Analysis》2009,19(1):137-190
We develop the theory of the “local” Hardy space
and John-Nirenberg space
when M is a Riemannian manifold with bounded geometry, building on the classic work of Fefferman-Stein and subsequent material,
particularly of Goldberg and Ionescu. Results include
–
duality, L
p
estimates on an appropriate variant of the sharp maximal function,
and bmo-Sobolev spaces, and action of a natural class of pseudodifferential operators, including a natural class of functions
of the Laplace operator, in a setting that unifies these results with results on L
p
-Sobolev spaces. We apply results on these topics to some interpolation theorems, motivated in part by the search for dispersive
estimates for wave equations.
相似文献
974.
Andreas H. Hamel 《Set-Valued and Variational Analysis》2009,17(2):153-182
It is proven that a proper closed convex function with values in the power set of a preordered, separated locally convex space
is the pointwise supremum of its set-valued affine minorants. A new concept of Legendre–Fenchel conjugates for set-valued
functions is introduced and a Moreau–Fenchel theorem is proven. Examples and applications are given, among them a dual representation
theorem for set-valued convex risk measures.
相似文献
975.
The paper deals with the study of Fredholm property and essential spectrum of general difference (or band) operators acting on the spaces l p (X) on a discrete metric space X periodic with respect to the action of a finitely generated discrete group. The Schrödinger operator on a combinatorial periodic graph is a prominent example of a band operator of this kind. 相似文献
976.
Bang-Yen Chen 《Central European Journal of Mathematics》2009,7(3):400-428
Submanifolds with parallel mean curvature vector play important roles in differential geometry, theory of harmonic maps as
well as in physics. Spatial surfaces in 4D Lorentzian space forms with parallel mean curvature vector were classified by B.
Y. Chen and J. Van der Veken in [9]. Recently, spatial surfaces with parallel mean curvature vector in arbitrary pseudo-Euclidean
spaces are also classified in [7]. In this article, we classify spatial surfaces with parallel mean curvature vector in pseudo-Riemannian
spheres and pseudo-hyperbolic spaces with arbitrary codimension and arbitrary index. Consequently, we achieve the complete
classification of spatial surfaces with parallel mean curvature vector in all pseudo-Riemannian space forms. As an immediate
by-product, we obtain the complete classifications of spatial surfaces with parallel mean curvature vector in arbitrary Lorentzian
space forms.
相似文献
977.
In this paper, we prove that the K?hler–Ricci flow converges to a K?hler–Einstein metric when E
1 energy is small. We also prove that E
1 is bounded from below if and only if the K-energy is bounded from below in the canonical class.
The first named author is partially supported by a NSF grant, while the third author was partially supported by a NSF supplement
grant. 相似文献
978.
On the spaces S p , an upper estimate is found for the norm of the error functional δ N (f) of cubature formulas possessing the Haar d-property in the two-dimensional case. An asymptotic relation is proved for $ \left\| {\delta _N (f)} \right\|_{S_p^* } On the spaces S
p
, an upper estimate is found for the norm of the error functional δ
N
(f) of cubature formulas possessing the Haar d-property in the two-dimensional case. An asymptotic relation is proved for with the number of nodes N ∼ 2
d
, where d → ∞. For N ∼ 2
d
with d → ∞, it is shown that the norm of δ
N
for the formulas under study has the best convergence rate, which is equal to N
−1/p
.
Original Russian Text ? K.A. Kirillov, M.V. Noskov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi
Fiziki, 2009, Vol. 49, No. 1, pp. 3–13. 相似文献
979.
研究了$\theta$型Calderon-Zygmund核的多线性奇异积分极大算子, 证明了这类极大算子的$L^{p}$-有界性. 相似文献
980.
通过引进锥对角拟凸概念, 讨论了Stampacchia 广义向量拟均衡问题解的存在性.由于该问题包含了许多形式的变分不等式与均衡问题作为特例,所得解的存在性结果推广和发展了近期的一些研究结果,主要有以下两个方面: 1)放宽了对连续性的要求; 2)由数值型推广到了向量型. 相似文献