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991.
992.
B. Yousefi 《Archiv der Mathematik》2004,83(6):536-539
Let
be a Hilbert space of functions analytic on a plane domain such that for every in the functional of evaluation at is bounded. Assume further that
contains the constants and admits multiplication by the independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive.Received: 17 February 2004 相似文献
993.
We classify the irreducible components of the varieties
\[
\V(n,a,b) = \{ (A,B) \in \M_n(\field) \times \M_n(\field) \mid
AB = BA = A^a = B^b = 0 \}.
\] 相似文献
994.
In this paper we compute the line integral of a complex function on a rectifiable cycle homologous to zero obtaining a Green’s
formula with multiplicities that involves the
of the function and the index of the cycle. We consider this formula in several settings and we obtain a sharp version in
terms of the Lebesgue integrability properties of the partial derivatives of the function. This result depends on the proven
fact that the index of a rectifiable cycle is square integrable with respect to the planar Lebesgue measure.
The work of both authors is partially supported by grants 2000SGR-00059, 2001SGR 00172 of Generalitat de Catalunya and BFM
2002-04072-C02-02 of Ministerio de Ciencia y Tecnologia 相似文献
995.
Manuel del Pino Jean Dolbeault Monica Musso 《Journal de Mathématiques Pures et Appliquées》2004,83(12):1405-1456
We consider the problem of finding positive solutions of Δu+λu+uq=0 in a bounded, smooth domain Ω in , under zero Dirichlet boundary conditions. Here q is a number close to the critical exponent 5 and 0<λ<λ1. We analyze the role of Green's function of Δ+λ in the presence of solutions exhibiting single and multiple bubbling behavior at one point of the domain when either q or λ are regarded as parameters. As a special case of our results, we find that if , where λ∗ is the Brezis-Nirenberg number, i.e., the smallest value of λ for which least energy solutions for q=5 exist, then this problem is solvable if q>5 and q−5 is sufficiently small. 相似文献
996.
This paper is concerned with the existence, smoothness and attractivity of invariant manifolds for evolutionary processes on general Banach spaces when the nonlinear perturbation has a small global Lipschitz constant and locally Ck-smooth near the trivial solution. Such a nonlinear perturbation arises in many applications through the usual cut-off procedure, but the requirement in the existing literature that the nonlinear perturbation is globally Ck-smooth and has a globally small Lipschitz constant is hardly met in those systems for which the phase space does not allow a smooth cut-off function. Our general results are illustrated by and applied to partial functional differential equations for which the phase space (where r>0 and being a Banach space) has no smooth inner product structure and for which the validity of variation-of-constants formula is still an interesting open problem. 相似文献
997.
Hong-Ming Yin 《Journal of Differential Equations》2004,200(1):137-161
In this paper we first study the regularity of weak solution for time-harmonic Maxwell's equations in a bounded anisotropic medium Ω. It is shown that the weak solution to the linear degenerate system, , is Hölder continuous under the minimum regularity assumptions on the complex coefficients γ(x) and ξ(x). We then study a coupled system modeling a microwave heating process. The dynamic interaction between electric and temperature fields is governed by Maxwell's equations coupled with an equation of heat conduction. The electric permittivity, electric conductivity and magnetic permeability are assumed to be dependent of temperature. It is shown that under certain conditions the coupled system has a weak solution. Moreover, regularity of weak solution is studied. Finally, existence of a global classical solution is established for a special case where the electric wave is assumed to be propagating in one direction. 相似文献
998.
Alzati A. Bertolini M. Besana G. 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2004,74(1):57-75
Smooth, complex, ruled surfaces embedded in ℙ5 as linearly normal scrolls, such that they are contained in a quadric cone, are considered. Rational scrolls and some elliptic
scrolls are shown to be the only ones contained in cones of rank 5. Results on scrolls contained in cones of lower ranks are
also obtained. 相似文献
999.
We consider here a model of fluid-structure evolution
problem which, in particular, has been largely studied from the
numerical point of view. We prove the existence of a strong
solution to this problem. 相似文献
1000.
For a Hall system of a finite solvable group G, it is known that the set
of -permutable subgroups is a sublattice of the subgroup lattice of G. We investigate the class SPM of groups in which the lattice
is modular. We prove that if
is modular, then U V for all
(an evidently stronger condition). Both of these phenomena—the modularity of
and whether two -permutable subgroups U and V permute with each other—are shown to be determined locally, by what happens at each prime. The class SPM is shown to be quotient closed, but not direct product or subgroup closed.This revised electronic version of the Abstract includes the formulas that were missing in the previous electronic version published online in September 2004. 相似文献