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Revista Matemática Complutense Nº 22

Nombre de la Revista: Revista Matemática Complutense
Número de Sumario: 22
Fecha de Publicación: 2009/1

Revista Matemática Complutense

Servicio de Publicaciones de la Universidad Complutense de Madrid 

Vol 22  Nº 1   (2009)

Más información/Texto completo en  http://revistas.ucm.es/portal/ ....


Contenidos - Contents    

Uniqueness of Entropy Solutions of Nonlinear Elliptic-Parabolic-Hyperbolic Problems in One Dimension Space  
OUARO, Stanislas

Palabras Clave: Elliptic; Parabolic; Hyperbolic; Weak solution; Entropy solution; L1-contraction
We consider a class of elliptic-parabolic-hyperbolic degenerate equations of the form b(u)t — a(u, φ(ux)x= f with homogeneous Dirichlet conditions and initial conditions. In this paper we prove an L1-contraction principle and the uniqueness of entropy solutions under rather general assumptions on the data. 


Renormalized Solutions for Nonlinear Degenerate Elliptic Problems with L1 Data  
AMMAR, Kaouther | REDWANE, Hicham

Palabras Clave: Renormalized solutions; Nonlinear degenerate elliptic equations; Weighted Sobolev spaces
We are interested in a class of nonlinear degenerate diffusion problems with a diffusion function a(x, u, Vu) which is not controlled with respect to u and which is not uniformly coercive on the weighted Sobolev spaces W1,p0 (Ω, w). Existence of a renormalized solution is proved in the L1-setting. 


Semistability of Certain Bundles on a Quintic Calabi-Yau Threefold  
BRAMBILLA, Maria Chiara

Palabras Clave: Semistability; Vector bundles
In a recent paper Douglas and Zhou aim for explicit examples of string theory compactifications that have a different number of generations and can be connected. For this purpose, they provide a list of bundles on a quintic Calabi-Yau threefold. They need to show that (at least some of) these bundles are semistable and leave this as an open question. In this paper we prove the semistability of most of the bundles in the list, thus completing the result of Douglas and Zhou. 


Solving Variational Inclusions by a Method Obtained Using a Multipoint Iteration Formula  
CABUZEL, Catherine | PIETRUS, Alain

Palabras Clave: Set-valued mapping; Generalized equations; Pseudo-Lipschitz maps; Multipoint iteration formula
This paper deals with variational inclusions of the form: 0 ε f(x)+F(x) where f is a single function admitting a second order Fréchet derivative and F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (xk) satisfying 0 ε f(xk)+∑M i=1 aiΛf(xk+βi(xk+1-xk))(xk+1-xk)+F(xk+1) where the single-valued function involved in this relation is an approximation of the function f based on a multipoint iteration formula and we show that this method is locally cubically convergent. 


A Discrete Hardy-Laptev-Weidl-Type Inequality and Associated Schrödinger-Type Operators   
EVANS, W. Desmond | SCHMIDT, Karl Michael

Palabras Clave: Discrete Schrödinger operator; Aharonov-Bohm magnetic potential
Although the classical Hardy inequality is valid only in the three- and higher dimensional case, Laptev and Weidl established a two-dimensional Hardy-type inequality for the magnetic gradient with an Aharonov-Bohm magnetic potential. Here we consider a discrete analogue, replacing the punctured plane with a radially exponential lattice. In addition to discrete Hardy and Sobolev inequalities, we study the spectral properties of two associated self-adjoint operators. In particular, it is shown that, for suitable potentials, the discrete Schrödingertype operator in the Aharonov-Bohm field has essential spectrum concentrated at 0, and the multiplicity of its lower spectrum satisfies a CLR-type inequality. 


Existence of Renormalized Solution of Some Elliptic Problems in Orlicz Spaces 
AHAROUCH, Lahsen | BENNOUNA, Jaouad | TOUZANI, Abdelfettah

Palabras Clave: Orlicz Sobolev spaces; Boundary value problems; Truncations; Renormalized
In this paper, we study the problem:—div a(x, u, ∆u) — div Φ(u) + g(x; u) = f in the framework of Orlicz spaces. The main contribution of our work is to prove the existence of a renormalized solution without any restriction on the N-function of the Orlicz space. 


On Dilation Operators in Besov Spaces  

Palabras Clave: Besov spaces; Dilation operators; Moment conditions
We consider dilation operators Tk : f → f(2k.) in the framework of Besov spaces Bsp,q (Rn) when 0 < p≤ 1. If s > n(1/p — 1) Tk is a bounded linear operator from Bsp,q (Rn) into itself and there are optimal bounds for its norm. We study the situation on the line s = n(1/p — 1), an open problem mentioned in [5, 2.3.1, 2.3.2]. It turns out that the results shed new light upon the diversity of different approaches to Besov spaces on this line, associated to definitions by differences, Fourier-analytical methods, and subatomic decompositions. 


Newton Binomial Formulas in Schubert Calculus  
CORDOVEZ, Jorge | GATTO, Letterio | SANTIAGO, Taíse

Palabras Clave: Schubert Calculus on a Grassmann algebra; Newton’s binomial formulas in Schubert calculus; Enumerative geometry of linear series on the projective line
We prove Newton’s binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points. 


Extremal Vector Valued Inequalities for Hankel Transforms  

Palabras Clave: Disc multiplier; Fourier-Hankel transforms
Boundary Sentinels with Given Sensitivity  
MASSENGO MOPHOU, Gisèle | PUEL, Jean-pierre

Palabras Clave: Heat equation; Optimal control; Controllability; Carleman inequalities; Sentinels
The notion of sentinels with given sensitivity was introduced by J.-L. Lions in [10] in order to identify parameters in a problem of pollution ruled by a semilinear parabolic equation. He proves that the existence of such sentinels is reduced to the solution of exact controllability problem with constraints on the state. Reconsidering this notion of sentinels in a more general framework, we prove the existence of the new sentinels by solving a boundary null-controllability problem with constraint on the control. Our results use a Carleman inequality which is adapted to the constraint. 


A Symbolic Calculus and a Parametrix Construction for Pseudodifferential Operators with Non-Smooth Negative Definite Symbols  
POTRYKUS, Alexander

Palabras Clave: Symbolic calculus; Non-smooth symbols; Negative definite functions; Feller semigroups
We consider pseudodifferential operators that have non-smooth negative definite symbols and develop a corresponding symbolic calculus. Combining this symbolic calculus with the use of non-smooth symbols that are asymptotically constant in the co-variable we succeed infunding a parametrix for a certain pseudodifferential equation. This in turn allows us to show that some pseudodifferential operators with non-smooth negative definite symbols are pregenerators of Feller semigroups. 


About the Banach Envelope of l1,∞ 
PIETSCH, Albrecht

Palabras Clave: Banach envelope; Marcinkiewicz space l1,∞; Weak l1-space
We study the Banach envelope of the quasi-Banach space l1,∞ consisting of all sequences x=(ξ k) with sn(x)=O(1/n), where (sn (x)) denotes the non-increasing rearrangement of x=(ξ k) The situation turns out to be much more complicated than that in the well-known case of the separable subspace lo1,∞, whose members are characterized by sn(x) =o(1/n). 


2-Microlocal Besov and Triebel-Lizorkin Spaces of Variable Integrability  
KEMPKA, Henning

Palabras Clave: Besov spaces; Triebel-Lizorkin spaces; 2-microlocal spaces; Variable smoothness; Variable integrability; Local means
We introduce 2-microlocal Besov and Triebel-Lizorkin spaces with variable integrability and give a characterization by local means. These spaces cover spaces of variable exponent, spaces of variable smoothness and weighted spaces that have been studied in recent years. 


Besov and Triebel-Lizorkin Spaces Related to Singular Integrals with Flag Kernels  
YANG, Dachun

Palabras Clave: Besov space; Triebel-Lizorkin space; Flag singular integral; Flag fractional integral; Littlewood-Paley operator; Dual space; Lifting; Embedding
Let s1, s2 Є (—1, 1) and s = (s1, s2). In this paper, the author introduces the Besov space Bspqq(R2) with p, q Є [1, ∞] and the Triebel-Lizorkin space Fspqq(R2) with p Є (1, ∞) and q Є (1, ∞] associated to singular integrals with flag kernels. Some basic properties, including their dual spaces, some equivalent norm characterizations via Littlewood-Paley functions, lifting properties and some embedding theorems, on these spaces are given. Moreover, the au thor obtains the boundedness of flag singular integrals and fractional integrals on these spaces. 


Erratum to “Feller Semigroups Obtained by Variable Order Subordination" (Rev. Mat. Complut. 20 (2007), no. 2, 293-307)  
EVANS, Kristian P. | JACOB, Niels

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