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1.
In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation with the critical situation that on g and p, where , is periodic and is bounded. 相似文献
2.
Summary We present an approximation method of a space-homogeneous transport equation which we prove is convergent. The method is very promising for numerical computation. Comparison of a numerical computation with an exact solution is given for the Master equation. 相似文献
3.
We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R3 such that every homeomorphism f of R3 which preserves K coincides with the identity on K. 相似文献
4.
The existence of an attractor for a 2D-Navier-Stokes system with delay is proved. The theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous. However, on some occasions, the attractors may attract not only in the pullback sense but in the forward one as well. Also, this formulation allows to treat, in a unified way, terms containing various classes of delay features (constant, variable, distributed delays, etc.). As a consequence, some results for the autonomous model are deduced as particular cases of our general formulation. 相似文献
5.
Multilinear interpolation is a powerful tool used in obtaining strong-type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak Lq estimate for a single index q (which may be less than one) and that all the adjoints of the multilinear operator are of similar nature, and thus they also satisfy the same weak Lq estimate. Under this assumption, in this note we give a general multilinear interpolation theorem which allows one to obtain strong-type boundedness for the operator (and all of its adjoints) for a large set of exponents. The key point in the applications we discuss is that the interpolation theorem can handle the case q?1. When q>1, weak Lq has a predual, and such strong-type boundedness can be easily obtained by duality and multilinear interpolation (cf. Interpolation Spaces, An Introduction, Springer, New York, 1976; Math. Ann. 319 (2001) 151; in: Function Spaces and Applications (Lund, 1986), Lecture Notes in Mathematics, Vol. 1302, Springer, Berlin, New York, 1988; J. Amer. Math. Soc. 15 (2002) 469; Proc. Amer. Math. Soc. 21 (1969) 441). 相似文献
6.
7.
Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges. 相似文献
8.
We prove the existence of solutions to nonlinear free boundary problem with singularities at given points. 相似文献
9.
We consider the Dirichlet problem for a class of anisotropic degenerate elliptic equations. New a priori estimates for solutions and for the gradient of solutions are established. Based on these estimates sufficient conditions guaranteeing the solvability of the problem are formulated. The results are new even in the semilinear case when the principal part is the Laplace operator. 相似文献
10.
E. Goering M. Justen J. Geissler U. Rüdiger M. Rabe G. Güntherodt G. Schütz 《Applied Physics A: Materials Science & Processing》2002,74(6):747-753
Highly a-axis-textured CrO2 films have been deposited on Al2O3 (0001) substrates by chemical vapor deposition. CrO2 has been found to have highly a-axis (010)-oriented columnar growth on a Cr2O3 (0001) initial layer. The six-fold surface symmetry of the Cr2O3 initial layer leads to three equivalent in-plane orientations of the a-axis-oriented CrO2 unit cell. We report Cr L2,3 X-ray magnetic circular dichroism data along the surface normal and at 60° off-normal sample orientation. For a 60° sample
alignment, a strong increase of the projected orbital moment could be observed for unoccupied majority t2g states using moment analysis. Therefore, the c axis is identified as the intrinsic magnetic easy axis of CrO2. In addition, a small spin moment and a very strong magnetic dipole term Tz have been found.
Received: 8 January 2002 / Accepted: 8 January 2002 相似文献