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41.
For a nonlinear programming problem with locally Lipschitz objective and inequality constraint functions and continuously differentiable equality constraint functions, a necessary and sufficient condition is presented for the set of multiplier vectors to be nonempty and bounded.This author's work was supported by the National Science Foundation under Grant No. MCS 78-06716. 相似文献
42.
Pierre Germain 《Journal of Differential Equations》2006,226(2):373-428
In this article, we describe spaces P such that: if u is a weak (in the sense of Leray [J. Leray, Sur le mouvement d'un fluide visqueux remplissant l'espace, Acta Math. 63 (1934) 193-248]) solution of the Navier-Stokes system for some initial data u0, and if u belongs to P, then u is unique in the class of weak solutions. We say then that weak-strong uniqueness holds. It turns out that the proof of such results relies on the boundedness of a trilinear functional , where α, β belong to [0,1]. In order to find optimal conditions for the boundedness of F, we are led to describing spaces of multipliers and of paramultipliers (that is, functions which map, by classical pointwise product or by paraproduct, a given Sobolev spaces in another given Sobolev space). The study of these spaces enables us to give conditions for weak-strong uniqueness which generalise all previously known results, from the famous Serrin criterion [J. Serrin, The initial value problem for the Navier-Stokes equations, in: R.E. Langer (Ed.), Nonlinear Problems, Univ. of Wisconsin Press, 1963, pp. 69-98], to the recent conditions formulated by Lemarié-Rieusset [P.-G. Lemarié-Rieusset, Recent Developments in the Navier-Stokes Problem, Chapman and Hall, 2003]. 相似文献
43.
Tuo-Yeong Lee 《Journal of Mathematical Analysis and Applications》2006,323(1):741-745
This paper is a continuation of the paper [T.Y. Lee, Product variational measures and Fubini-Tonelli type theorems for the Henstock-Kurzweil integral, J. Math. Anal. Appl. 298 (2004) 677-692], in which we proved several Fubini-Tonelli type theorems for the Henstock-Kurzweil integral. Let f be Henstock-Kurzweil integrable on a compact interval . For a given compact interval , set
44.
Susana Coré 《Journal of Mathematical Analysis and Applications》2010,370(2):472-485
Let G be a homogeneous group with homogeneous dimension Q, and let So denote the space of Schwartz functions on G with all moments vanishing. Let be the usual Euclidean Fourier transform. For j∈R, we let be the space of J, smooth away from 0, satisfying |α∂J(ξ)|?Cβ|ξ|j−|β|, where both |ξ| and |β| are taken in the homogeneous sense. We characterize , and show that as elements of . If j1,j2,j1+j2>−Q, one can replace So, by S, S′ in this result. A key ingredient of our proof is a lemma from the fundamental wavelet paper from 1985 by Frazier and Jawerth [4]. We believe that, in turn, our result will be useful in the theory of wavelets on homogeneous groups. 相似文献
45.
本文主要回顾了单调算子理论与分裂算法的基本概念和结果,重点介绍Forward-Backward分裂算法和Douglas-Rachford分裂算法的收敛性理论及应用.同时,也介绍了这些方法处理非凸优化问题的最新进展以及一些前沿和热点问题.最后提出了几个未来可以继续研究的方向. 相似文献
46.
Space-time Estimates for Parabolic Type Operator and Application to Nonlinear Parabolic Equations
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In this present paper we establish space-time estimates of solutions for linear parabolic type equations based on classical multipliers theory or operator semigroup theory. According to space-time estimates we first construct suitable work space L^q(0, T; L^P), moreover we study the Cauchy problem and initial boundary value problem for semilinear parabolic equation in L^q(0, T; L^P) type space. 相似文献
47.
We theoretically establish the existence status of some previously open abelian difference sets. More precisely, we show the nonexistence of all the following difference sets: (841,120,17) in Z29×Z29, (364,121,40) in Z2×Z2×Z7×Z13, (837,133,21) in Z3×Z3×Z3×Z31,Z3×Z9×Z31 and Z837. 相似文献
48.
If T is any bounded linear operator on Besov spaces Bpσj,qj(Rn)(j=0,1, and 0<σ1<σ<σ0), it is proved that the commutator [T,Tμ]=TTμ−TμT is bounded on Bpσ,q(Rn), if Tμ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded variation on dyadic coronas. 相似文献
49.
P.G. Lemarié-Rieusset S. Gala 《Journal of Mathematical Analysis and Applications》2006,322(2):1030-1054
We characterize the pointwise multipliers which maps a Sobolev space to a Sobolev space in the case |s|<r<d/2. 相似文献
50.
Sadek Gala 《Journal of Mathematical Analysis and Applications》2006,323(2):1253-1263
In this paper, we characterize the class of measurable functions (or, more generally, real- or complex-valued distributions) f such that the commutator operator
Cf=[f,Δ] 相似文献