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131.
Zdeněk Skalák 《Applications of Mathematics》2003,48(2):153-159
We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution u belongs to L
(0, T, L
3()3), then the set of all possible singular points of u in is at most finite at every time t0 (0,T). 相似文献
132.
In this paper we show that the parabolic problem associated with elliptic operators A having coefficients in has the property of maximal -regularity.
RID="h1"
ID="h1"In Memoriam Philippe Bénilan 相似文献
133.
Wei-Shyan Tai 《Proceedings of the American Mathematical Society》2001,129(3):699-711
In this paper a capacitary weak type inequality for Sobolev functions is established and is applied to reprove some well-known results concerning Lebesgue points, Taylor expansions in the -sense, and the Lusin type approximation of Sobolev functions.
134.
Gancho Tachev 《Journal of Computational Analysis and Applications》2001,3(4):361-381
A direct theorem for approximation by algebraic polynomials in two variables with different degrees in each variable in Lp-metric (1 p ) on rectangles is proved, and the dependence of the constants on various parameters is studied. 相似文献
135.
Hamilton equations based not only upon the Poincaré–Cartan equivalent of a first-order Lagrangian, but also upon its Lepagean equivalent are investigated. Lagrangians which are singular within the Hamilton–De Donder theory, but regularizable in this generalized sense are studied. Legendre transformation for regularizable Lagrangians is proposed and Hamilton equations, equivalent with the Euler–Lagrange equations, are found. It is shown that all Lagrangians affine or quadratic in the first derivatives of the field variables are regularizable. The Dirac field and the electromagnetic field are discussed in detail. 相似文献
136.
Jos M. Rodríguez 《Journal of Approximation Theory》2001,108(2):119
We characterize the set of functions which can be approximated by polynomials with the following norm
for a big class of weights w0, w1, …, wk 相似文献
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137.
Quasi-P*-maps and P(, , )-maps defined in this paper are two large classes of nonlinear mappings which are broad enough to include P*-maps as special cases. It is of interest that the class of quasi-P*-maps also encompasses quasimonotone maps (in particular, pseudomonotone maps) as special cases. Under a strict feasibility condition, it is shown that the nonlinear complementarity problem has a solution if the function is a nonlinear quasi-P*-map or P(, , )-map. This result generalizes a classical Karamardian existence theorem and a recent result concerning quasimonotone maps established by Hadjisawas and Schaible, but restricted to complementarity problems. A new existence result under an exceptional regularity condition is also established. Our method is based on the concept of exceptional family of elements for a continuous function, which is a powerful tool for investigating the solvability of complementarity problems. 相似文献
138.
A nonlinear integral operator T of the form (Tf)(s)=∫G K(t, f (σ(s, t))) dμ(t), for sG, is defined and investigated in the measure space (G, Σ, μ), where f and K are vector-valued functions with values in normed linear spaces E and F, respectively. The results are applied to the case of integro-differential operators in generalized Orlicz–Sobolev spaces. There are studied problems of existence, embeddings, and approximation by means of T. 相似文献
139.
In this paper, we study orthogonal polynomials with respect to the bilinear form (f, g)
S
= V(f) A
V(g)
T
+ <u, f
(N)
g
(N)V(f) =(f(c
0), f "(c
0), ..., f
(n – 1)
0(c
0), ..., f(c
p
), f "(c
p
), ..., f
(n – 1)
p(c
p
))
u is a regular linear functional on the linear space P of real polynomials, c
0, c
1, ..., c
p
are distinct real numbers, n
0, n
1, ..., n
p
are positive integer numbers, N=n
0+n
1+...+n
p
, and A is a N × N real matrix with all its principal submatrices nonsingular. We establish relations with the theory of interpolation and approximation. 相似文献
140.
The evolution Boussinesq equations describe the evolution of the temperature and velocity fields of viscous incompressible Newtonian fluids. Very often, they are a reasonable model to render relevant phenomena of flows in which the thermal effects play an essential role. In the paper we prescribe non-Dirichlet boundary conditions on a part of the boundary and prove the existence and uniqueness of solutions to the Boussinesq equations on a (short) time interval. The length of the time interval depends only on certain norms of the given data. In the proof we use a fixed point theorem method in Sobolev spaces with non-integer order derivatives. The proof is performed for Lipschitz domains and a wide class of data. 相似文献